Composition Functions

When you apply a function rule to the result of another function rule you compose a function.

-you MUST know the notation to compose.

Notation: f(g)(x)= f(g(x))
pronounce- “f of g of x”
f composed of g composed of x.

-all functions are composed of x, x is the input.

f(g(x)) is the same as (fog)(x)

f(x)= x^2+4 g(x)= 2x+3

now instead of putting x as the input, put g(x).
f(g(x))=(2x+3) then apply all of the x values from the x problem
f(g(x))= (2x+3)^2+4
simplify
=(2x+3)(2x+3)+4
=4x^2+6x+9+4
f(g(x))= 4x^2+12x+13

Ex1: Find (gof)(2)
=g(f(2))
1. Always work inside out by plugging the input values in.
=g(f(2))= g(8)