# Math Help - Constructing Even and Odd Functions

1. ## Constructing Even and Odd Functions

Hi there, thanks for any help in advance.

Been stuck on this for a while, wondering if there is a printing error as I cant make it work!

Separate the function x^2 − 3^x into odd and even parts.

I get f(-x) to be -x^2 - 3^-x

Giving, 1/2[(x^2-3^x)+(-x^2-3^-x) = 1/2(-3^x-3^-x) for the even part

but the text book says the answer is x2 −1/2(3^x + 3^−x).

I think they may have got the f(-x) wrong but cant be sure!

Any hints greatly apprieciated!

Mike

2. Originally Posted by mikewhant
Separate the function x^2 − 3^x into odd and even parts.
Any function can be written as the sum of an even function and an odd function.

For any $g(x)=\underbrace {\frac{g(x)+g(-x)}{2}}_{\text{even}}+\underbrace {\frac{g(x)-g(-x)}{2}}_{\text{odd}}$.