Aim: What is the composition of functions? Do Now: Given: Express z in terms of x HW: Work sheet

We can apply one function into another function. This process is called composition of functions Let and g(x) = x + 1 ○ The notation is the symbol ○ is read “of ”. f(g(x)) = When we evaluate composition of functions, we go from inside to outside.

How do we compose f(x) = 2x + 3 and g(x) = x – 1? g is the inside function and f is the outside function. When you compute the composition, you compute the inside function first and then plug that result into the outside function.

Examples Notice that g is the inside function and f is the outside function. Let Then

If f(x) = 3x – 1 and g(x) = 2x, evaluate First of all, we evaluate g(2) = 2(2) = 4 Then we evaluate f(4) = 3(4) – 1 = 12 – 1 = 11 If f(x) = 4x, g(x) = 3x + 1, evaluate f(g(-1)) g(–1) = 3(–1) + 1 = – = – 2 f(–2) = 4(–2) = –8

Examples Let Evaluate: a. f(g(x)) b. g(f(x))

Example If Evaluate 3. 4.