Practice Inverse Function in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The inverse of a function f is a function f^{-1} that reverses f: if f(a) = b then f^{-1}(b) = a. It exists only when f is one-to-one.

If f turns a into b, then f^{-1} turns b back into a. Reverse the process.

Example 1

easy
Find the inverse of f(x) = 3x - 7.

Example 2

medium
Find the inverse of f(x) = \frac{2x + 5}{x - 1} for x \neq 1.

Example 3

easy
Find the inverse of f(x) = \frac{x}{4} + 2.

Example 4

hard
If f(x) = 2^x, find f^{-1}(x). Then verify by showing that f(f^{-1}(8)) = 8.