Question 1

Which of the following statements best describes a one-to-one function?

Accepted Answer

Each $y$ in the range is paired with only one $x$ in the domain.

Question 2

Which test can be used to determine if a function is one-to-one?

Accepted Answer

Horizontal Line Test

Question 3

Given the function $f(x) = 2x + 5$, what is the equation of its inverse?

Accepted Answer

$f^{-1}(x) = \frac{x-5}{2}$

Question 4

If $f(x) = x^3 + 2$, which of the following is the inverse function $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x) = \sqrt[3]{x - 2}$

Question 5

Suppose $f(x) = \sqrt{x - 2}$ for $x \geq 2$. What is the domain of the inverse function $f^{-1}(x)$?

Accepted Answer

$x \geq 0$

Question 6

Given $f(x) = \frac{2x + 3}{x - 4}$, which of the following is the correct inverse function $f^{-1}(x)$?

Question 7

Which of the following pairs of functions are inverses of each other?

Accepted Answer

$f(x) = e^x$ and $g(x) = \ln(x)$

Question 8

A function $f$ passes the Horizontal Line Test. What does this imply about $f$?

Accepted Answer

$f$ is a one-to-one function.

Question 9

Given the function $f(x) = 2x - 9$ used to encode a message, what is the inverse function used to decode the message?

Accepted Answer

$f^{-1}(x) = \frac{x - 9}{2}$

Question 10

If $f(x)$ and $g(x)$ are inverse functions, which of the following must be true for all $x$ in the domain of $f$?

Accepted Answer

$f(g(x)) = x$ and $g(f(x)) = x$

Question 11

Which of the following functions is NOT one-to-one?

Accepted Answer

$f(x) = x^2$ (for all real $x$)

Question 12

Given the graph of $f(x)$, which of the following describes the graph of its inverse $f^{-1}(x)$?

Accepted Answer

It is a reflection of $f(x)$ over the line $y = x$.

Question 13

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 14

Which step is NOT part of the process for finding the equation of an inverse function?

Accepted Answer

Differentiate the function

Question 15

If $f(x) = 3x - 7$, and you encode a message using this function, what is the formula to decode the message?

Accepted Answer

$f^{-1}(x) = \frac{x - 7}{3}$

Question 16

Which of the following is a necessary condition for a function to have an inverse?

Accepted Answer

The function must be one-to-one.

Question 17

Given $f(x) = x^5 + 1$, what is the inverse function $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x) = \sqrt[5]{x - 1}$

Question 18

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

Accepted Answer

$f^{-1}(x) = x^2 - 2$

Question 19

A hospital uses the function $f(x) = 2x - 9$ to encode patient IDs. If a patient’s encoded ID is 31, what was the original ID?

Accepted Answer

15

Inverse Functions: One-to-One Functions and Their Applications

Study Guide - Practice Questions