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?

2)( rrA

http://www.youtube.com/watch?v=gdTBdyNtHUg&feature=related

So what do we need to know first?

Composition Functions can be denoted:

or

)(xfg fg

gf

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).

)(xgf

If 32)( xxf 2)( xxg and

What will g(f(x)) look like?

x f(x)

-2

0

2

4

6

f(x) g(f(x))

Complete the following tables:

Practice Algebraically

Given the functions:

53)( xxf2)1(2)( xxg

Find these values:

f(4) g(4) f(g(4)) g(f(4)) g(-1) g(f(-1))

Algebraic Challenge:

Find f(g(x)):

2)(

63)(2

xxg

xxf

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))