Composite Functions
A composite function is the conjoining of two (or more)
functions by replacement of a variable in one equation with
another function. A composite may be notated as either
𝑓 𝑔 𝑥 or 𝑓 ∘ 𝑔 𝑥 . In both cases, a function 𝑔 𝑥 is
substituted into 𝑓 𝑥 .
1. If 𝑔 𝑥 =
𝑓 ℎ −1 .
40 −
1 2
𝑥
2
and ℎ 𝑥 = 4 𝑥 − 1 evaluate
2. Given 𝑓 𝑥 = 𝑥 + 6
a) 𝑓 𝑔 𝑥
2
𝑥
2
− 1 and 𝑔 𝑥 = + 4 find;
b) 𝑔 ∘ 𝑓 𝑥
c) 𝑓 −1 𝑔 𝑥
3. State the domain of the composite function 𝑓 ℎ 𝑥
1
𝑓 𝑥 =
and ℎ 𝑥 = 𝑥 − 3.
where
𝑥+2
4. Express 𝑦 = 𝑥 + 1
𝑓 and 𝑔.
3
− 9 as the composition of two functions
? pg. 152 #2abcd, 2, 3defghi, 4 – 9, 11