Precalculus Inverse Functions Test with Point Values (PDF)
This inverse functions test for Precalculus covers inverse functions (Common Core F-BF.B.4a, F-BF.B.4b, F-BF.B.4c, F-BF.B.4d), with a free PDF to print.
Time and points
- Grade: Precalculus
- Chapter: Inverse Functions
- Standards: F-BF.B.4a, F-BF.B.4b, F-BF.B.4c, F-BF.B.4d
- Time: 45 minutes
- Total: 20 points
Inverse functions test: questions
Question 1 – Horizontal line test [2 pts]
Does the graph represent a one-to-one function? Explain using the horizontal line test.
Question 2 – Inverse of a line [2 pts]
Find \(f^{-1}(x)\) if \(f(x)=\frac{2x-5}{3}\).
Question 3 – Inverse of a root function [2 pts]
Find \(f^{-1}(x)\) for \(f(x)=\sqrt{x+3}\) and state its domain.
Question 4 – Verify inverses [2 pts]
Show that \(f(x)=5x-2\) and \(g(x)=\frac{x+2}{5}\) are inverses.
Question 5 – Points on an inverse [3 pts]
(a) List the coordinates of three points on \(f^{-1}\). (b) Find \(f^{-1}(x)\) for \(f(x)=\frac{x}{2}+1\). (c) Explain how the graphs of \(f\) and \(f^{-1}\) are related.
Question 6 – Rational inverse [2 pts]
Find \(f^{-1}(x)\) for \(f(x)=\frac{x+1}{x-2}\).
Question 7 – Restricted domain [2 pts]
Restrict \(f(x)=(x+1)^{2}-4\) to \(x\ge -1\) and find \(f^{-1}(x)\).
Question 8 – Car value model [3 pts]
The value of Sofia’s car is \(V(t)=28{,}000-2{,}000t\) dollars after \(t\) years. (a) Find \(V^{-1}\). (b) Use it to find when the value is \(\$17{,}000\). (c) State what \(V^{-1}\) represents.
Question 9 – Domain and range of an inverse [2 pts]
Let \(f(x)=\sqrt{x-5}+2\). Find \(f^{-1}(x)\) and state its domain.
Key facts behind this inverse functions test
- f^-1(f(x)) = x and f(f^-1(x)) = x.
- Find an inverse: write y = f(x), swap x and y, solve for y.
- Domain of f becomes the range of f^-1, and the range of f becomes the domain of f^-1.
- The graph of f^-1 is the reflection of the graph of f over y = x.
- Restrict the domain of a function that is not one-to-one, such as x^2 with x >= 0.
How to use this inverse functions test
Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.
All Precalculus chapters: Precalculus math.
