Lesson 1.6 Inverse Functions. Inverse Function, f -1 (x): Domain consists of the range of the original function Range consists of the domain of the original.

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Presentation transcript:

Lesson 1.6 Inverse 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

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