1. Combinations of Functions:
1.8
Combinations of Functions:
Composite Functions
The composition of the functions f and g is
“f composed by g of x equals f of g of x”

2. Ex. f(x) =
g(x) = x - 1
Find
of 2
Ex. f(x) = x and g(x) = 4 – x Find:
f(g(x)) = (4 – x2) + 2
= -x2 + 6
g(f(x)) = 4 – (x + 2)2
= 4 – (x2 + 4x + 4)
= -x2 – 4x

3. Ex. Express h(x) = as a composition
of two functions f and g.
f(x) =
g(x) =
x - 2

4. Find the sum, difference, and quotient of two functions.
f(x) = 2x g(x) = x2 + 2x - 1
(f + g)(x) =
2x x2 + 2x - 1 =
x2 + 4x
(f - g)(x) =
2x (x2 + 2x - 1) =
-x2 + 2