Lesson 1.6Inverse Functions

Inverse Function, f -1(x):

Domain consists of the range of the original function

Range consists of the domain of the original function

f(f -1(x)) = x

Graphs of Inverses

Symmetric about line y = x

ExampleAre these inverses?

Finding an Inverse Function:

►Ordered Pairs → Exchange the domain (x) and range (y) values

► Basic Function → Re-write the function using inverse operations

► Any Function →

■ Replace f(x) with y

■ Switch x and y

■ Solve for new y

■ Replace new y with f -1(x)

► Graph → Use line y = x to reflect

Existence of an Inverse Function

For an inverse to be a function:

Original function must be one-to-one

“y-values may not repeat”

“Inverse is a function”

Horizontal Line Test