Question 1

What is the range of the function $f(x) = |x|$?

Accepted Answer

Correct Option: A. Solution: The modulus function $f(x) = |x|$ returns the absolute value of $x$, so the range is all non-negative real numbers: $\{x \mid x \geq 0\}$.

Question 2

For the rational function $f(x) = \frac{x^2 - 4}{x + 2}$, what is the domain?

Accepted Answer

Correct Option: B. Solution: The domain of a rational function excludes values that make the denominator zero. Here, $x + 2 = 0$ when $x = -2$, so $x = -2$ is excluded from the domain.

Question 3

If $f(x) = x^2 + 5x + 6$, what are the roots of the function?

Accepted Answer

Correct Option: A. Solution: The roots of the quadratic equation $x^2 + 5x + 6 = 0$ can be found using factoring: $(x + 2)(x + 3) = 0$, giving roots $x = -2$ and $x = -3$.

Question 4

Let $f(x) = |x|$ be the modulus function. What is the range of $f(x)$?

Accepted Answer

Correct Option: B. Solution: The modulus function $f(x) = |x|$ outputs the absolute value of $x$, which is always non-negative. Therefore, the range is all non-negative real numbers.

Question 5

Given the function $f(x) = |x|$, which of the following describes its graph?

Accepted Answer

Correct Option: B. Solution: The function $f(x) = |x|$ forms a V-shaped graph with the vertex at the origin, as it equals $x$ for $x \geq 0$ and $-x$ for $x < 0$.

Question 6

For the function $f(x) = \lfloor x \rfloor$, which of the following is true?

Accepted Answer

Correct Option: B. Solution: The function $f(x) = \lfloor x \rfloor$ is the greatest integer function, and its graph consists of horizontal steps at each integer value.

Question 7

Which of the following represents the identity function?

Accepted Answer

Correct Option: A. Solution: The identity function is defined as $f(x) = x$ for all $x$ in the domain.

Question 8

Consider the function $f(x) = x^2$. What is the range of this function?

Accepted Answer

Correct Option: A. Solution: The function $f(x) = x^2$ is a parabola opening upwards, so its range is all non-negative real numbers.

Question 9

What is the value of the greatest integer function $[x]$ when $x = 2.7$?

Accepted Answer

Correct Option: A. Solution: The greatest integer function $[x]$ returns the greatest integer less than or equal to $x$. For $x = 2.7$, $[x] = 2$.

Question 10

If $$f(x) = \frac{x^2 - 1}{x - 1}$$, what is the simplified form of $f(x)$ for $x 
eq 1$?

Accepted Answer

Correct Option: A. Solution: For $x 
eq 1$, the expression simplifies to $f(x) = \frac{(x-1)(x+1)}{x-1} = x + 1$.

Question 11

If $f(x) = x^2$ and $g(x) = 2x + 1$, what is the result of the operation $(f + g)(x)$?

Accepted Answer

Correct Option: A. Solution: The sum of two functions $f(x)$ and $g(x)$ is given by $(f + g)(x) = f(x) + g(x) = x^2 + 2x + 1$.

Question 12

Consider the function $f(x) = \frac{x^2 - 4}{x - 2}$. Which of the following statements correctly describes the domain of this function?

Accepted Answer

Correct Option: A. Solution: The function $f(x) = \frac{x^2 - 4}{x - 2}$ simplifies to $f(x) = x + 2$ for all $x 
eq 2$. Hence, the domain excludes $x = 2$ where the denominator becomes zero.

Question 13

Consider the function $f(x) = [x]$. What is the value of $f(2.999)$?

Accepted Answer

Correct Option: A. Solution: The greatest integer function $[x]$ returns the greatest integer less than or equal to $x$. For $x = 2.999$, the greatest integer less than or equal to $x$ is $2$.

Question 14

Consider the sets $P = \{a, b, c\}$ and $Q = \{Ali, Bhanu, Binoy, Chandra, Divya\}$. If a relation $R$ from $P$ to $Q$ is defined as $R = \{(x, y): x 	ext{ is the first letter of the name } y, x \in P, y \in Q\}$, which of the following correctly represents the range of $R$?

Accepted Answer

Correct Option: A. Solution: The range of a relation is the set of all second elements in the ordered pairs. Here, $R = \{(a, Ali), (b, Bhanu), (b, Binoy), (c, Chandra)\}$, so the range is \{Ali, Bhanu, Binoy, Chandra\}.

Question 15

Which of the following is a real-valued function?

Accepted Answer

Correct Option: D. Solution: All the given functions are real-valued as they map real numbers to real numbers.

Question 16

Which of the following statements is correct about the greatest integer function $f(x) = [x]$?

Accepted Answer

Correct Option: B. Solution: The greatest integer function $[x]$ returns the greatest integer less than or equal to $x$, creating a step-like graph.

Question 17

Given sets $A = \{x, y\}$ and $B = \{1, 2, 3\}$, which of the following represents $B 	imes A$?

Accepted Answer

Correct Option: A. Solution: The Cartesian product $B 	imes A$ is the set of all ordered pairs $(b, a)$ where $b \in B$ and $a \in A$. Thus, $B 	imes A = \{(1, x), (1, y), (2, x), (2, y), (3, x), (3, y)\}$.

Question 18

What is the output of the modulus function for a negative input value?

Accepted Answer

Correct Option: C. Solution: The modulus function outputs the absolute value of a number, so for a negative input, it returns the positive equivalent.

Question 19

Which of the following statements is true regarding Cartesian products?

Accepted Answer

Correct Option: B. Solution: If either $A$ or $B$ is the null set, then $A 	imes B$ will also be an empty set, i.e., $A 	imes B = \emptyset$.

Question 20

If $A = \{1, 2, 3\}$ and $B = \{4, 5\}$, what is the Cartesian product $A 	imes B$?

Accepted Answer

Correct Option: A. Solution: The Cartesian product $A 	imes B$ consists of all ordered pairs where the first element is from set $A$ and the second element is from set $B$.

Question 21

For the function $f(x) = \frac{1}{x}$, what is the range?

Accepted Answer

Correct Option: B. Solution: The range of $f(x) = \frac{1}{x}$ is all real numbers except 0, as $f(x)$ can never be zero.

Question 22

Consider the function $f(x) = \frac{1}{x}$ defined for all real numbers except zero. What is the range of this function?

Accepted Answer

Correct Option: A. Solution: The function $f(x) = \frac{1}{x}$ is undefined at $x = 0$, and its range is all real numbers except zero, as the function can take any real value except zero.

Question 23

Consider the function $f(x) = \frac{1}{x}$ defined for all real numbers except zero. Which of the following statements is true about its domain and range?

Accepted Answer

Correct Option: A. Solution: The function $f(x) = \frac{1}{x}$ is defined for all real numbers except zero, and its range is also all real numbers except zero.

Question 24

Given the rational function $$f(x) = \frac{3x + 2}{x - 5}$$, determine the horizontal asymptote.

Accepted Answer

Correct Option: B. Solution: The horizontal asymptote of a rational function $$\frac{ax + b}{cx + d}$$ is $$y = \frac{a}{c}$$ if the degrees of the numerator and denominator are equal. Here, it is $y = \frac{3}{1} = 3$.

Question 25

For the rational function $$f(x) = \frac{x^2 + 4x + 4}{x + 2}$$, what is the hole in the graph of the function?

Accepted Answer

Correct Option: A. Solution: The function has a hole at $x = -2$ because the factor $(x + 2)$ cancels out in the numerator and denominator, indicating a removable discontinuity.

Question 26

What is the Cartesian product of two sets $A = \{1, 2\}$ and $B = \{3, 4\}$?

Accepted Answer

Correct Option: A. Solution: The Cartesian product $A 	imes B$ is the set of all ordered pairs $(a, b)$ where $a \in A$ and $b \in B$. Thus, $A 	imes B = \{(1, 3), (1, 4), (2, 3), (2, 4)\}$.

Question 27

Which of the following statements correctly defines a function?

Accepted Answer

Correct Option: A. Solution: A function is defined as a special type of relation where each element in the domain is associated with exactly one element in the codomain.

Question 28

What is the total number of relations that can be defined from a set $A$ with 3 elements to a set $B$ with 2 elements?

Accepted Answer

Correct Option: B. Solution: The total number of relations from set $A$ to set $B$ is given by the number of subsets of the Cartesian product $A 	imes B$. Since $n(A) = 3$ and $n(B) = 2$, $n(A 	imes B) = 3 	imes 2 = 6$. Therefore, the number of relations is $2^6$.

Question 29

If $A = \{1, 2\}$ and $B = \{3, 4\}$, which of the following is a valid subset of the Cartesian product $A 	imes B$?

Accepted Answer

Correct Option: A. Solution: The Cartesian product $A 	imes B$ consists of ordered pairs where the first element is from $A$ and the second element is from $B$. Thus, $\{(1, 3), (2, 4)\}$ is a valid subset.

Question 30

If $f(x) = [x]$, what is the value of $f(-2.3)$?

Accepted Answer

Correct Option: A. Solution: The greatest integer function $[x]$ returns the greatest integer less than or equal to $x$. For $x = -2.3$, $[x] = -3$.

Question 31

Which of the following functions is not a polynomial?

Accepted Answer

Correct Option: C. Solution: The function $h(x) = \frac{1}{x}$ is not a polynomial because it involves division by $x$, which is not allowed in polynomial functions.

Question 32

Consider the rational function $$f(x) = \frac{2x^2 + 3x - 2}{x^2 - 4}$$. What are the values of $x$ for which the function is undefined?

Accepted Answer

Correct Option: A. Solution: The function is undefined where the denominator is zero. Solving $x^2 - 4 = 0$ gives $x = 2$ and $x = -2$.

Question 33

If $h(x) = \frac{x^2 - 1}{x - 1}$, determine the domain of $h(x)$.

Accepted Answer

Correct Option: A. Solution: The function $h(x) = \frac{x^2 - 1}{x - 1}$ simplifies to $h(x) = x + 1$ for $x 
eq 1$. Therefore, the domain is all real numbers except $x = 1$.

Question 34

For the greatest integer function $f(x) = [x]$, which of the following statements is correct?

Accepted Answer

Correct Option: B. Solution: The greatest integer function $f(x) = [x]$ is discontinuous at integer values of $x$ because it jumps to the next integer at each integer point.

Question 35

Consider the rational function $f(x) = \frac{1}{x}$. Which of the following statements is true?

Accepted Answer

Correct Option: A. Solution: The rational function $f(x) = \frac{1}{x}$ is undefined at $x = 0$ because division by zero is undefined.

Question 36

Which of the following represents the Cartesian product $A 	imes B$ if $A = \{1, 2\}$ and $B = \{3, 4\}$?

Accepted Answer

Correct Option: A. Solution: The Cartesian product $A 	imes B$ is the set of all ordered pairs where the first element is from $A$ and the second is from $B$. Thus, $A 	imes B = \{(1, 3), (1, 4), (2, 3), (2, 4)\}$.

Question 37

Given two sets $P = \{a, b\}$ and $Q = \{1, 2, 3\}$, how many relations can be defined from $P$ to $Q$?

Accepted Answer

Correct Option: D. Solution: The total number of relations from $P$ to $Q$ is the number of subsets of the Cartesian product $P 	imes Q$. Since $n(P) = 2$ and $n(Q) = 3$, $n(P 	imes Q) = 6$. Therefore, the number of relations is $2^6 = 64$.

Question 38

Which of the following relations is a function?

Accepted Answer

Correct Option: A. Solution: Option A is a function because each element in the domain has exactly one image in the codomain.

Question 39

Evaluate the greatest integer function for $x = -2.7$.

Accepted Answer

Correct Option: A. Solution: For $x = -2.7$, the greatest integer less than or equal to $x$ is $-3$, hence $[-2.7] = -3$.

Question 40

Given two functions $f(x) = x^2$ and $g(x) = 3x + 1$, find the expression for the function $(f + g)(x)$.

Accepted Answer

Correct Option: A. Solution: The sum of two functions $f(x)$ and $g(x)$ is given by $(f + g)(x) = f(x) + g(x) = x^2 + 3x + 1$.

Question 41

Which of the following is a polynomial function?

Accepted Answer

Correct Option: A. Solution: A polynomial function is defined by an expression of the form $a_0 + a_1x + a_2x^2 + ... + a_nx^n$, where $n$ is a non-negative integer and coefficients are real numbers. Both $f(x)$ and $g(x)$ fit this form, but $h(x)$ and $k(x)$ do not.

Question 42

For sets $A = \{1, 2\}$ and $B = \{3, 4\}$, which of the following statements is true?

Accepted Answer

Correct Option: B. Solution: While the sets $A 	imes B$ and $B 	imes A$ are not equal, they have the same number of elements, hence $n(A 	imes B) = n(B 	imes A) = 4$.

Question 43

Given two sets $A = \{1, 2\}$ and $B = \{3, 4, 5\}$, what is the cardinality of the Cartesian product $A 	imes B$?

Accepted Answer

Correct Option: D. Solution: The cardinality of the Cartesian product $A 	imes B$ is given by $n(A 	imes B) = n(A) \cdot n(B) = 2 \cdot 3 = 6$.

Question 44

Consider the sets $A = \{1, 2, 3\}$ and $B = \{4, 5\}$. If a relation $R$ from $A$ to $B$ is defined such that $R = \{(x, y) \mid x + y = 6, x \in A, y \in B\}$, which of the following ordered pairs is in the relation $R$?

Accepted Answer

Correct Option: B. Solution: The relation $R$ is defined by $x + y = 6$. Checking each option: (1, 5) gives $1 + 5 = 6$, (2, 4) gives $2 + 4 = 6$, (3, 3) gives $3 + 3 = 6$, and (2, 5) gives $2 + 5 = 7$. Only (2, 4) satisfies the condition.

Question 45

Given the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x) = x^2$, which of the following statements is true about the domain and range of $f$?

Accepted Answer

Correct Option: B. Solution: The function $f(x) = x^2$ is defined for all real numbers, so the domain is $\mathbb{R}$. Since $x^2$ is always non-negative, the range is $[0, \infty)$.

Question 46

Consider the function $f(x) = |x|$. Which of the following statements about its graph is true?

Accepted Answer

Correct Option: C. Solution: The graph of the modulus function $f(x) = |x|$ is V-shaped with the vertex at the origin, consisting of two linear segments: $y = x$ for $x \geq 0$ and $y = -x$ for $x < 0$.

Question 47

If $A = \{a, b, c\}$ and $B = \{1, 2\}$, what is the cardinality of the Cartesian product $A 	imes B$?

Accepted Answer

Correct Option: C. Solution: The cardinality of the Cartesian product $A 	imes B$ is given by $n(A 	imes B) = n(A) \cdot n(B)$. Here, $n(A) = 3$ and $n(B) = 2$, so $n(A 	imes B) = 3 	imes 2 = 6$.

Question 48

If $A = \{x \mid 1 \leq x \leq 3\}$ and $B = \{y \mid 2 \leq y \leq 4\}$, which of the following is the Cartesian product $A 	imes B$?

Accepted Answer

Correct Option: A. Solution: The Cartesian product $A 	imes B$ consists of all possible ordered pairs where the first element is from $A$ and the second element is from $B$. Thus, $A 	imes B = \{(1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)\}$.

Question 49

Consider the polynomial function $f(x) = x^3 - 3x^2 + 4x - 5$. What is the remainder when $f(x)$ is divided by $x - 2$?

Accepted Answer

Correct Option: C. Solution: By the Remainder Theorem, the remainder of $f(x)$ divided by $x - 2$ is $f(2)$. Calculating $f(2) = 2^3 - 3(2)^2 + 4(2) - 5 = 8 - 12 + 8 - 5 = 7$.

Question 50

If $A = \{a, b\}$ and $B = \{1, 2\}$, which of the following is not an element of the Cartesian product $A 	imes B$?

Accepted Answer

Correct Option: C. Solution: The Cartesian product $A 	imes B$ consists of pairs where the first element is from $A$ and the second is from $B$. Since $3$ is not in $B$, $(b, 3)$ is not an element of $A 	imes B$.

Question 51

Given the signum function $f(x) = 	ext{sgn}(x)$, which of the following is true about its range?

Accepted Answer

Correct Option: A. Solution: The signum function $f(x) = 	ext{sgn}(x)$ outputs -1 for negative $x$, 0 for $x = 0$, and 1 for positive $x$, thus its range is $\{-1, 0, 1\}$.

Question 52

If $h(x) = 2x^3 - 5x^2 + 4x - 1$ is a polynomial function, what is the leading coefficient of its derivative $h'(x)$?

Accepted Answer

Correct Option: A. Solution: The derivative $h'(x) = 6x^2 - 10x + 4$. The leading coefficient is 6.

Question 53

Consider the function $f(x) = |x|$ defined for all real numbers. Which of the following statements about the modulus function is correct?

Accepted Answer

Correct Option: A. Solution: The modulus function $f(x) = |x|$ is continuous for all real numbers, but it is not differentiable at $x = 0$. It has a minimum value of 0 at $x = 0$ but is not strictly increasing as it decreases for $x < 0$ and increases for $x > 0$.

Question 54

For the function $f(x) = x^2 + 5x - \frac{3}{x + 1}$, identify the domain.

Accepted Answer

Correct Option: A. Solution: The function $f(x) = x^2 + 5x - \frac{3}{x + 1}$ is undefined at $x = -1$ because it causes division by zero. Thus, the domain is all real numbers except $x = -1$.

Question 55

If the signum function is applied to a number $x = -5$, what will be the output?

Accepted Answer

Correct Option: C. Solution: The signum function indicates the sign of a number. For $x = -5$, the output is -1 as the number is negative.

Question 56

Given a polynomial $g(x) = x^4 - 4x^3 + 6x^2 - 4x + 1$, identify the nature of its roots.

Accepted Answer

Correct Option: B. Solution: The polynomial $g(x)$ can be rewritten as $(x - 1)^4$, indicating that all roots are real and repeated at $x = 1$.

Question 57

If $A 	imes B = \{(p, q), (p, r), (m, q), (m, r)\}$, what are the sets $A$ and $B$?

Accepted Answer

Correct Option: A. Solution: The set $A$ consists of the first elements of the pairs, and $B$ consists of the second elements. Hence, $A = \{p, m\}$ and $B = \{q, r\}$.

Question 58

Consider the sets $P = \{x \mid x > 0\}$ and $Q = \{y \mid y < 0\}$. What can be said about the Cartesian product $P 	imes Q$?

Accepted Answer

Correct Option: C. Solution: In the Cartesian product $P 	imes Q$, the first element comes from $P$ (positive) and the second from $Q$ (negative), so it contains pairs where the first element is positive and the second is negative.

Question 59

If a relation $R$ on the set of natural numbers $N$ is defined by $R = \{(x, y) : y = 2x, x, y \in N\}$, which of the following is true about $R$?

Accepted Answer

Correct Option: A. Solution: The relation $R = \{(x, y) : y = 2x, x, y \in N\}$ is a function because every natural number $x$ has a unique image $2x$, satisfying the definition of a function.

Question 60

In the mapping diagram from set $P = \{a, b, c\}$ to set $Q = \{Ali, Bhanu, Binoy, Chandra, Divya\}$, which of the following mappings makes it a function?

Accepted Answer

Correct Option: A. Solution: Option A is a function because each element in set $P$ is mapped to exactly one element in set $Q$.

Question 61

What is the domain of the function $f(x) = \sqrt{x-1}$?

Accepted Answer

Correct Option: A. Solution: The domain of $f(x) = \sqrt{x-1}$ is $x \geq 1$ because the expression under the square root must be non-negative.

Question 62

Let $R$ be a relation from set $A = \{1, 2, 3\}$ to set $B = \{4, 5, 6\}$ defined by $R = \{(x, y) \mid x < y\}$. Which of the following pairs is NOT in $R$?

Accepted Answer

Correct Option: D. Solution: For a pair $(x, y)$ to be in $R$, $x$ must be less than $y$. Checking the options, (1, 4), (2, 5), and (3, 6) satisfy $x < y$, but (3, 5) does not since $3 
ot< 5$. Hence, (3, 5) is not in $R$.

Question 63

Given the function $f(x) = \sqrt{9 - x^2}$, what is the domain of $f(x)$?

Accepted Answer

Correct Option: B. Solution: The function $f(x) = \sqrt{9 - x^2}$ is defined when the expression under the square root is non-negative, i.e., $9 - x^2 \geq 0$. Solving this inequality gives $x \in [-3, 3]$.

Question 64

Consider the relation $R = \{(x, y) : x 	ext{ is the first letter of the name } y, x \in P, y \in Q\}$. If $P = \{a, b, c\}$ and $Q = \{Ali, Bhanu, Binoy, Chandra, Divya\}$, what is the range of $R$?

Accepted Answer

Correct Option: A. Solution: The range of a relation is the set of all second elements in the ordered pairs. For the given relation, the range is $\{Ali, Bhanu, Binoy, Chandra\}$.

Relations and Functions

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Cartesian Product of Sets

Relations

Functions

Algebra of Functions

Polynomial Functions

Rational Functions

Modulus and Signum Functions

Greatest Integer Function

Domain and Range of Real Functions

Function Testing and Mapping Diagrams

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Cartesian Product of Sets

Relations

Functions

Algebra of Functions

Polynomial Functions

Rational Functions

Modulus and Signum Functions

Greatest Integer Function

Domain and Range of Real Functions

Function Testing and Mapping Diagrams

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Multiple Choice Questions

Q1.What is the range of the function f(x)=∣x∣f(x) = |x|f(x)=∣x∣?

Correct Answer: A

Q2.For the rational function f(x)=x2−4x+2f(x) = \frac{x^2 - 4}{x + 2}f(x)=x+2x2−4​, what is the domain?

Correct Answer: B

Q3.If f(x)=x2+5x+6f(x) = x^2 + 5x + 6f(x)=x2+5x+6, what are the roots of the function?

Correct Answer: A

Q4.Let f(x)=∣x∣f(x) = |x|f(x)=∣x∣ be the modulus function. What is the range of f(x)f(x)f(x)?

Correct Answer: B

Q5.Given the function f(x)=∣x∣f(x) = |x|f(x)=∣x∣, which of the following describes its graph?

Correct Answer: B

Q6.For the function f(x)=⌊x⌋f(x) = \lfloor x \rfloorf(x)=⌊x⌋, which of the following is true?

Correct Answer: B

Q7.Which of the following represents the identity function?

Correct Answer: A

Q8.Consider the function f(x)=x2f(x) = x^2f(x)=x2. What is the range of this function?

Correct Answer: A

Q9.What is the value of the greatest integer function [x][x][x] when x=2.7x = 2.7x=2.7?

Correct Answer: A

Q10.If f(x)=x2−1x−1f(x) = \frac{x^2 - 1}{x - 1}f(x)=x−1x2−1​, what is the simplified form of f(x)f(x)f(x) for x≠1x \neq 1x=1?

Correct Answer: A

Q11.If f(x)=x2f(x) = x^2f(x)=x2 and g(x)=2x+1g(x) = 2x + 1g(x)=2x+1, what is the result of the operation (f+g)(x)(f + g)(x)(f+g)(x)?

Correct Answer: A

Q12.Consider the function f(x)=x2−4x−2f(x) = \frac{x^2 - 4}{x - 2}f(x)=x−2x2−4​. Which of the following statements correctly describes the domain of this function?

Correct Answer: A

Q13.Consider the function f(x)=[x]f(x) = [x]f(x)=[x]. What is the value of f(2.999)f(2.999)f(2.999)?

Correct Answer: A

Correct Answer: A

Q15.Which of the following is a real-valued function?

Correct Answer: D

Q16.Which of the following statements is correct about the greatest integer function f(x)=[x]f(x) = [x]f(x)=[x]?

Correct Answer: B

Q17.Given sets A={x,y}A = \{x, y\}A={x,y} and B={1,2,3}B = \{1, 2, 3\}B={1,2,3}, which of the following represents B×AB \times AB×A?

Correct Answer: A

Q18.What is the output of the modulus function for a negative input value?

Correct Answer: C

Q19.Which of the following statements is true regarding Cartesian products?

Correct Answer: B

Q20.If A={1,2,3}A = \{1, 2, 3\}A={1,2,3} and B={4,5}B = \{4, 5\}B={4,5}, what is the Cartesian product A×BA \times BA×B?

Correct Answer: A

Q21.For the function f(x)=1xf(x) = \frac{1}{x}f(x)=x1​, what is the range?

Correct Answer: B

Q22.Consider the function f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ defined for all real numbers except zero. What is the range of this function?

Correct Answer: A

Q23.Consider the function f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ defined for all real numbers except zero. Which of the following statements is true about its domain and range?

Correct Answer: A