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Math Help - Constructing Even and Odd Functions

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by mikewhant View Post
    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}}.
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