Inverse Functions The inverse of a function is obtained by interchanging the x and y values of the original function. Inverse Function Notation: If the original function is f(x) then the Inverse Function is f -1 (x) CAUTION f -1 (x) does not mean f(x) raised to the negative first power. It means the inverse function of f(x).

Inverse Relations and Inverse Functions f(x) = (1, 4) (2, 3) (3, -2) (4, -5) f -1 (x) = (4, 1) (3, 2) (-2, 3) (-5, 4) f -1 (x) is a function g(x) = (5, 3) (4, 2) (3, 2) (2, 3) g -1 (x) = (3, 5) (2, 4) (2, 3) (3, 2) g -1 (x) is NOT a function Only one-to-one functions have inverse functions

Equations of Inverse Functions Replace f(x) with y Interchange x and y Solve for y That was easy

Checking Inverse Functions If f(x) and g(x) are inverse functions, then f(g(x)) = x and g(f(x)) = x Holy schnikies, it works!

More Checking Inverse Functions Find the inverse of f(x) and then verify that they are actually inverses. So easy, even a caveman can do it.

Graphing Inverse Functions Find the inverse of f(x) and then graph the original function and the inverse.