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Lesson 1.6 Inverse Functions

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. Example Are these inverses?.

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Lesson 1.6 Inverse Functions

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  1. Lesson 1.6Inverse Functions

  2. 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

  3. Graphs of Inverses Symmetric about line y = x Example Are these inverses?

  4. 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

  5. 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

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