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Functions: CompositionSolutions
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) = x^{2} + 2x. Then
(c) 27x^{3
}
Answer Let f(x) = 3x and let g(x) = x^{3}. 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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