Inverse functions

Objective

Find and verify the inverse of a one-to-one function.

What it means

The inverse function f^-1 undoes what f does: if f(a) = b, then f^-1(b) = a. To find it algebraically, swap x and y in the equation and solve for the new y.

Key terms

One-to-one function

Each output comes from exactly one input; passes horizontal line test

Inverse function

f^-1(x) reverses f(x)

Rules to remember

• Swap x and y, then solve for y to find the inverse.
• f(f^-1(x)) = x and f^-1(f(x)) = x verify an inverse.
• The graphs of f and f^-1 are reflections across y = x.

Step by step

1. 1Replace f(x) with yWrite y = expression.
2. 2Swap x and yExchange the variables.
3. 3Solve for yIsolate y to get f^-1(x).