1. Replace inside with “x” of other function
(f g)(x) = f(g(x))
f(x)= x + 1 g(x) = 2x -1
f(g(x))
Inside first
2x–1
( ) + 1
Replace inside with “x” of other function X 2x
evaluate 2x

2. Replace inside with “X” of other function
(f g)(x) = f(g(x))
f(x) = x g(x) = 2x + 1 2
f(g(x))
Inside First
( )
2x + 1 2
Replace inside with “X” of other function X
Evaluate
(2x + 1)(2x + 1)
4x + 4x + 1 2

3. g(x) = x + 1 f(x) = x - 2 (g f)(x) = g(f(x)) ( ) + 1 x - 2
( ) + 1
x - 2 2
(x-2)(x-2) + 1

4. h(x) = x + 2x -1 g(x) = 4x -5 h g(x)) (4x – 5) (4x – 5) +2 -1 2
(4x – 5)(4x – 5) +8x – 10 -1
16x – 20x – 20x x 2
16x -32x +14 2

5. f(x) = 2x -x -4 g(x) = -5x + 4 f g (x) 2 - -4 (-5x + 4) (-5x + 4)
(-5x + 4) (-5x + 4) 2
2(-5x + 4)(-5x + 4) +5x -4 -4
2(25x -20x -20x + 16) +5x -4 -4 2
50x -40x -40x x -4 -4 2
50x -75x +24 2

6. f(x) = 2x -x +4 g(x) = 5x + 3 (g f)(x) g(f(x)) 5( ) +3 2x – x + 4
5( ) +3
2x – x + 4 3
10x -5x 3
10x -5x + 23 3

7. Application
Pick up “ How to”