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General Mathematics
Composition of Functions
For all values of x for which both f() and g() are defined, we define the following as:
󰇛
󰇜󰇛
󰇜
󰇛
󰇛
󰇜
󰇜
In general, the notation 󰇛
󰇛
󰇜
󰇜, read as “ of of ,” means composed with of ” can be
written as
󰇛
󰇜󰇛
󰇜
.
Illustrative Examples:
Given the functions
󰇛
󰇜
and
󰇛
󰇜
, find the following:
a.
󰇛
󰇜󰇛
󰇜
󰇛
󰇜󰇛
󰇜

󰇛
󰇜
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
󰇛
󰇜󰇛
󰇜

󰇛
󰇜󰇛
󰇜

b.
󰇛
󰇜󰇛
󰇜
󰇛
󰇜󰇛
󰇜

󰇛
󰇜
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
󰇛
󰇜󰇛
󰇜
󰇛
󰇜󰇛
󰇜
c.
󰇛
󰇜󰇛
󰇜
󰇛
󰇜󰇛
󰇜

󰇛
󰇜󰇛
󰇜
󰇛󰇜
󰇛
󰇜󰇛
󰇜
Alternative Solution:
󰇛
󰇜󰇛
󰇜
󰇛
󰇛
󰇜
󰇜
󰇛
󰇜
󰇛
󰇜

󰇛
󰇜
󰇛
󰇜
󰇛
󰇜
󰇛󰇜
󰇛
󰇜
󰇛
󰇜󰇛
󰇜
d.
󰇛
󰇜󰇛

󰇜
󰇛
󰇜󰇛
󰇜
󰇛
󰇜󰇛

󰇜
󰇛󰇜
󰇛
󰇜
󰇛󰇜
e.
󰇛
󰇜󰇛
󰇜

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General Mathematics Composition of Functions For all values of x for which both f(𝑥) and g(𝑥) are defined, we define the following as: (𝑓 ∘ 𝑔)(𝑥) = 𝑓(𝑔(𝑥)) In general, the notation 𝑓(𝑔(𝑥)), read as “𝑓 of 𝑔 of 𝑥,” means “𝑓 composed with 𝑔 of 𝑥” can be written as (𝑓 ∘ 𝑔)(𝑥). Illustrative Examples: Given the functions 𝑔(𝑥) = 𝑥 2 − 1 and ℎ(𝑥) = 𝑥 + 1, find the following: a. (𝒈 ∘ 𝒉)(𝒙) (𝑔 ∘ ℎ)(𝑥) = 𝑔(ℎ(𝑥)) (𝑔 ∘ ℎ)(𝑥) = 𝑔(𝑥 + 1) (𝑔 ∘ ℎ)(𝑥) = (𝑥 + 1)2 ? ...
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Anonymous
Very useful material for studying!

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