Functions: Composition-Solutions
Compute:
.
Answer
Answer
Answer
4. Write as a composition of two functions :
Answer Let 
and
let g(x) = x + 1. Then
Answer Let 
and
let g(x) = x2 + 2x. Then
(c) 27x3
Answer Let f(x) = 3x and let g(x) = x3. Then
Answer Let 
and let g(x)
= 2x + 2. Then
5. Write as a composition of three functions:
Answer Let 
. Then
Answer Let 
. Then
Answer Let 
. Then
We say that a function f(x) is the inverse of a function g(x) if
6. Verify that the given functions are inverses of each other.
Answer
Since f(g(x)) = x = g(f(x)) the functions f(x) and g(x)
are indeed inverses of
one another
Answer
Therefore, 
, as desired.
Answer
Clearly, 
by the same
calculation and therefore 
as desired.
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