Inverse Functions

Definition: Two functions f and g are inverses of one another provided that

· All ordered pairs are interchanged.

· The graphs are symmetrical about the line y = x.

· f[g(x)] = x for each x in the domain of g

· g[f(x)] = x for each x in the domain of f.

Notation: If f and g are inverse functions of one another then

g(x) = f^-1(x)

and

f(x) = g^-1(x).

To find f^-1(x) for the function y = f(x) use a technique called

Switch and Solve:

1. Interchange x and y in the equation y = f(x).

2. Solve the resulting equation for y.

3. The resulting y = f^-1(x).