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Math Help - even function

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    even function

    f(x)=2x^2+2mx+12
    If f(x-3) is even, what is the value of "m"?
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  2. #2
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    Re: even function

    Do you mean f(x-3) is an even function?
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    Re: even function

    Quote Originally Posted by kastamonu View Post
    f(x)=2x^2+2mx+12
    If f(x-3) is even, what is the value of "m"?
    Did you consider just multiplying it out?
    f(x- 3)= 2x^2- 12x+ 9+ 2mx- 6m+ 12= 2x^2+(2m- 12)x+ 21- 6m.

    A polynomial function is even if and only if it has only even powers of x.
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    Re: even function

    Quote Originally Posted by Prove It View Post
    Do you mean f(x-3) is an even function?
    Yes.
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    Re: even function

    Quote Originally Posted by HallsofIvy View Post
    Did you consider just multiplying it out?
    f(x- 3)= 2x^2- 12x+ 9+ 2mx- 6m+ 12= 2x^2+(2m- 12)x+ 21- 6m.

    A polynomial function is even if and only if it has only even powers of x.
    Then (2m- 12)=0?
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    Re: even function

    Eventually, you will have to think for yourself!
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    Re: even function

    Quote Originally Posted by HallsofIvy View Post
    Did you consider just multiplying it out?
    f(x- 3)= 2x^2- 12x+ 9+ 2mx- 6m+ 12= 2x^2+(2m- 12)x+ 21- 6m.

    A polynomial function is even if and only if it has only even powers of x.
    That is not true. A function is even if \displaystyle \begin{align*} f(-x) = f(x) \end{align*} for all x.

    Consider the function \displaystyle \begin{align*} f(x) = (x - 1)^2 \end{align*}, then \displaystyle \begin{align*} f(-x) = (-x-1)^2 \neq (x-1)^2 \end{align*}.

    The OP needs to check what f(x-3) is and then set it equal to f( -(x-3) ).
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    Re: even function

    Quote Originally Posted by Prove It View Post
    That is not true. A function is even if \displaystyle \begin{align*} f(-x) = f(x) \end{align*} for all x.

    Consider the function \displaystyle \begin{align*} f(x) = (x - 1)^2 \end{align*}, then \displaystyle \begin{align*} f(-x) = (-x-1)^2 \neq (x-1)^2 \end{align*}.
    Yes, and (x- 1)^2= x^2- 2x+ 1 has x to an odd power.

    The OP needs to check what f(x-3) is and then set it equal to f( -(x-3) ).
    No, that would check if f is even. The OP needs to check if f(x- 3)= f(-x-3).
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    Re: even function

    f(x- 3)= f(-x-3)? Why do I have to check in this way?
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