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Math Help - function is even, odd, or neither?

  1. #1
    Member realintegerz's Avatar
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    function is even, odd, or neither?

    How would I go about doing that?

    Let's say f(x) = 17x^322 for example....
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by realintegerz View Post
    How would I go about doing that?

    Let's say f(x) = 17x^322 for example....
    To say so, find f(-x)

    Here, f(-x)=17*(-x)^{322}=17*((-1)*x)^{322}

    Using this rule : (ab)^c=a^c b^c, we get

    f(-x)=17*x^{322}*(-1)^{322}=f(x)*(-1)^{322}

    Using the rule of exponents : a^{bc}=(a^b)^c, we can say that (-1)^{322}=[(-1)^2]^{161}=1^{161}=1

    Thus f(-x)=f(x)


    Got it ?
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  3. #3
    Member realintegerz's Avatar
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    so if f(-x) = f(x) it is even, and if it doesnt it is odd?

    how do i know when its neither...
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  4. #4
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    Quote Originally Posted by realintegerz View Post
    so if f(-x) = f(x) it is even, and if it doesnt it is odd?

    how do i know when its neither...
    NO!

    Even: f(-x) = f(x).

    Odd: f(-x) = - f(x).

    Otherwise neither even nor odd.
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