# 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) = 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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