Question 1

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

Accepted Answer

A function where no two different elements in the domain map to the same element in the range.

Question 2

Given $f(x) = 3x - 2$, what is the inverse function $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x) = \frac{x-2}{3}$

Question 3

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

Accepted Answer

Horizontal Line Test

Question 4

If $f(x) = x^3$, is $f$ a one-to-one function? Why?

Accepted Answer

Yes, because no two different numbers have the same cube.

Question 5

Suppose $f(1) = 5$, $f(3) = 7$, and $f(8) = -10$. What is $f^{-1}(7)$?

Accepted Answer

$3$

Question 6

Which property must be satisfied for $f$ and $f^{-1}$ to be true inverses?

Accepted Answer

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

Question 7

If a pizza costs $p = 12 + 2n$ dollars, where $n$ is the number of toppings, what does the inverse function $f^{-1}(p)$ represent?

Accepted Answer

The number of toppings for a pizza that costs $p$ dollars.

Question 8

Find the inverse of the rational function $f(x) = \frac{2x+3}{x-1}$.

Question 9

If the graph of $f$ is reflected over the line $y = x$, what does the resulting graph represent?

Accepted Answer

The graph of the inverse function $f^{-1}(x)$.

Question 10

Given $f(x) = \sqrt{x-2}$, what is the inverse function $f^{-1}(x)$?

Accepted Answer

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

Question 11

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

Accepted Answer

A function that fails the horizontal line test is one-to-one.

Question 12

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

Accepted Answer

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

Question 13

A function $f$ is defined on domain $A$ and range $B$. If $f$ is one-to-one, what is true about its inverse $f^{-1}$?

Accepted Answer

$f^{-1}$ maps $B$ to $A$ and is also one-to-one.

Question 14

If $f(x)$ is a decreasing function, what can be said about its one-to-one property?

Accepted Answer

It is always one-to-one.

Question 15

If $f(x) = 12 + 2x$ models the price of a pizza with $x$ toppings, how many toppings does a pizza costing $22$ dollars have?

Accepted Answer

$5$

Question 16

Which of the following is the correct cancellation property for inverse functions?

Accepted Answer

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

One-to-One Functions and Their Inverses: College Algebra Study Notes

Study Guide - Practice Questions