# To check: Whether h = f ∘ g is always an even function if g is even. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.3, Problem 63E
To determine

## To check: Whether h=f∘g is always an even function if g is even.

Expert Solution

The composition function h=fg is always an even function.

### Explanation of Solution

Given:

The function g(x) is an even function.

The composite function, h(x)=(fg)(x) .

Verification:

Since g(x) is an even function, g(x)=g(x) .

Find the value of h(x) .

h(x)=(fg)(x)=f(g(x))=f(g(x))              [g(x)=g(x)]=h(x)

Thus, h(x)=h(x)

Therefore, it can be concluded that the composite function h=fg is always an even function.

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