Question 1

Given the function $f(x) = \dfrac{1}{x-2}$, what is the domain of $f$?

Accepted Answer

$x 
eq 2$

Question 2

If $f(x) = 4x + 1$ and $g(x) = \dfrac{x}{x-2}$, what is $(f \circ g)(x)$?

Accepted Answer

$\dfrac{5x-2}{x-2}$

Question 3

Which of the following functions is one-to-one?

Accepted Answer

$f(x) = x^3$

Question 4

Given $F(C) = \dfrac{9}{5}C + 32$, what does $F(100)$ represent in a real-world context?

Accepted Answer

The temperature in Fahrenheit when it is 100 degrees Celsius

Question 5

Which of the following is the correct definition of a one-to-one function?

Accepted Answer

A function $f$ is one-to-one if $f(x_1) = f(x_2)$ implies $x_1 = x_2$.

Question 6

If $C(F) = \dfrac{5}{9}(F-32)$, what is $C(212)$ and what does it mean?

Accepted Answer

$C(212) = 100$, which means 212 degrees Fahrenheit is 100 degrees Celsius

Question 7

Which of the following graphs passes the Horizontal Line Test?

Accepted Answer

A graph of $y = x^3$

Question 8

Given $f(x) = 2x + 3$ and $g(x) = \dfrac{x-3}{2}$, are $f$ and $g$ inverse functions?

Accepted Answer

Yes, because $f(g(x)) = x$ and $g(f(x)) = x$

Question 9

What is the range of the function $f(x) = \dfrac{1}{x-2}$?

Accepted Answer

All real numbers except $0$

Question 10

If $f(x)$ is a one-to-one function, what can be said about its inverse $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x)$ is also a function and is one-to-one

Question 11

Which statement is true about the composition cancellation equations for inverse functions?

Accepted Answer

$f(f^{-1}(x)) = x$ for all $x$ in the domain of $f^{-1}$

Question 12

Given the piecewise function $f(x) = \begin{cases} 2x+4 & x \leq -1 \ 2x-6 & x \geq 4 \end{cases}$, which of the following is true?

Accepted Answer

The function is not one-to-one because it shares $y$ values for different $x$

Question 13

If the graph of $f(x)$ passes the Horizontal Line Test, what does this imply?

Accepted Answer

The function is one-to-one

Question 14

Which of the following is the correct process to sketch the graph of the inverse of a one-to-one function $f(x)$?

Accepted Answer

Reflect the graph of $f(x)$ over the line $y = x$

Question 15

If $f(x) = x^2$ for $x \geq 0$, what is the inverse function $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x) = \sqrt{x}$

Question 16

Suppose $f(x)$ and $g(x)$ are inverse functions. If $f(7) = 3$, what is $g(3)$?

Accepted Answer

$g(3) = 7$

Question 17

Which of the following is NOT a property of inverse functions?

Accepted Answer

$f(x)$ and $f^{-1}(x)$ always have the same domain and range

Question 18

A function $f$ is defined on the domain $(-\infty, \infty)$ and is strictly increasing. Which statement is true?

Accepted Answer

$f$ is one-to-one and has an inverse function

Functions, One-to-One Functions, and Inverse Functions in College Algebra

Study Guide - Practice Questions