Take out Pencil Calculator Do now sheet Do

Take out: Pencil, Calculator, Do now sheet Do Now: 1) Simplify Agenda • Do Now • Composition and Inverse Functions • HW: Handout-composition and inverses Objective: Graph composite functions and compose functions Determine the inverse of a function

Composition of Functions Inverse Functions

Introduction • Value fed to first function • Resulting value fed to second function • End result taken from second function

Introduction • Notation for composition of functions: • Alternate notation:

Try It Out • Given two functions: § p(x) = 2 x + 1 § q(x) = x 2 - 3 • Then p ( q(x) ) = § p (x 2 - 3) = § 2 (x 2 - 3) + 1 = § 2 x 2 - 5 • Try determining q ( p(x) )

Decomposition of Functions Someone once dug up Beethoven's tomb and found him at a table busily erasing stacks of papers with music writing on them. They asked him. . . "What are you doing down here in your grave? " He responded, "I'm de-composing!!" But, seriously folks. . . Consider the following function which could be a composition of two different functions.

Decomposition of Functions • The function could be decomposed into two functions, k and j

Now You Try!!!

Inverse Functions • Inverse Notation Does not mean f to the -1 of x, It means inverse of f(x)

How to find the inverse

Verifying Inverses • If you can do the composition of the functions both ways (f(g(x)) and g(f(x))) and the solution is x for both, then the functions are inverses.

Verifying Inverses Continued • • • For example: f(x) = 2 x - 4 and g(x) = x/2+ 2 f(f-1(x)) = 2(x/2 + 2) - 4 =x+4– 4 = x correct

Try It! • Find the inverse