Algebra II Recipe: Inverse of a Function

A. Finding the Inverse of a Function

Switch the x and y variables only.

Solve the equation for y. (f^-1 indicates the inverse)

Graph the equation to determine if the inverse is a function.

Examples:

Find the inverse of y = 2x - 4

Find the inverse of f(x) = (1/2)x³ - 2

B. Verifying Two Functions are Inverses

Given f(x) and g(x), if f[g(x)] = x and g[f(x)] = x, then the functions are inverses.

Example:

Verify that f(x) = 2x + 1 and g(x) = (1/2)x - (1/2) are inverses.