Composition of Functions!!! Objective: I will be able to answer various forms of composition problems.

If a circle is continuously expanding, how can we measure the area over time? What is the formula for area of a circle? So what do we need to know first?

Composition Functions can be denoted: or f(x) is the outside function, and g(x) is the inside function, so the answer of g(x) becomes the input for f(x). g(x) is the outside function, and f(x) is the inside function, so the answer of f(x) becomes the input for g(x).

If and What will g(f(x)) look like? xf(x) f(x)g(f(x)) Complete the following tables:

Practice Algebraically Given the functions: Find these values: f(4) g(4) f(g(4)) g(f(4)) g(-1) g(f(-1))

Algebraic Challenge: Find f(g(x)):

Partner Practice With a partner write two equations Label one as f(x) and one as g(x) Find various values: –f(g(3)) –f(g(-2)) –g(f(4)) –g(f(-3))