# To prove : that if f and g are both even and odd function, then the sum if one is odd and one is even

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.5, Problem 91E
To determine

## To prove : that if f and g are both even and odd function, then the sum if one is odd and one is even

Expert Solution

### Explanation of Solution

Given information : The question is

f+g Necessarily even and if both are odd, is their sum necessarily odd

Proof : f(x) and g(x) are even function

f(x)=f(x) and g(x)=g(x)

g(x)+f(x)=g(x)+f(x)

So, the sum of two even function is necessary even function

f(x) And g(x) are odd function

f(x)=f(x)&g(x)=g(x)g(x)+f(x)=g(x)+(f(x))

So, The sum of two odd function is necessary odd function

Let f(x) is even function

And g(x) is odd function

g(x)+f(x)=g(x)+f(x)

So, the sum of even and odd function is neither even or nor odd

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