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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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