Let $\displaystyle f_1(x)$ and $\displaystyle f_2(x)$ be odd and even functions respectively. How can we construct an even function out of these?

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- Jul 4th 2010, 08:33 PMroshanheroFunctions
Let $\displaystyle f_1(x)$ and $\displaystyle f_2(x)$ be odd and even functions respectively. How can we construct an even function out of these?

- Jul 4th 2010, 09:49 PMdrumist
Plenty of ways, but why can't you just take $\displaystyle f_2(x)$ as the even function? What's the point of using $\displaystyle f_1(x)$ in constructing an even function?

Edit: In case you mean you need to construct an even function from only $\displaystyle f_1(x)$, some simple ways would be to take the absolute value or square the function.

$\displaystyle g(x)=|f_1(x)|$

$\displaystyle h(x)=(f_1(x))^2$

These would both be even functions. - Jul 5th 2010, 05:11 AMHallsofIvy
What does "construct out of them"

**mean**? - Jul 5th 2010, 05:13 AMHallsofIvy
- Jul 5th 2010, 07:29 AMMathelogician
Also their composition{ g(x) = f1(f2(x)) and h(x) = f2(f1(x)) } are even!