f(x)=2x^2+2mx+12

If f(x-3) is even, what is the value of "m"?

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- Apr 25th 2013, 05:29 AMkastamonueven function
f(x)=2x^2+2mx+12

If f(x-3) is even, what is the value of "m"? - Apr 25th 2013, 05:35 AMProve ItRe: even function
Do you mean f(x-3) is an even function?

- Apr 25th 2013, 06:49 AMHallsofIvyRe: even function
- Apr 25th 2013, 08:00 AMkastamonuRe: even function
- Apr 25th 2013, 08:01 AMkastamonuRe: even function
- Apr 25th 2013, 12:50 PMHallsofIvyRe: even function
Eventually, you will have to think for yourself!

- Apr 25th 2013, 03:52 PMProve ItRe: even function
That is not true. A function is even if $\displaystyle \displaystyle \begin{align*} f(-x) = f(x) \end{align*}$ for all x.

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

The OP needs to check what f(x-3) is and then set it equal to f( -(x-3) ). - Apr 25th 2013, 03:57 PMHallsofIvyRe: even function
- Apr 25th 2013, 10:27 PMkastamonuRe: even function
f(x- 3)= f(-x-3)? Why do I have to check in this way?