# Functions

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• Jul 4th 2010, 08:33 PM
roshanhero
Functions
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 PM
drumist
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 AM
HallsofIvy
What does "construct out of them" mean?
• Jul 5th 2010, 05:13 AM
HallsofIvy
Quote:

Originally Posted by drumist
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.

And if you really have to use both functions, so would \$\displaystyle |f_1(x)|+ f_2(x)\$ and \$\displaystyle (f_1(x))^2+ f_2(x)\$.

Now, if the problem had been to construct an even function from two odd functions, that would have been a little more interesting!
• Jul 5th 2010, 07:29 AM
Mathelogician
Also their composition{ g(x) = f1(f2(x)) and h(x) = f2(f1(x)) } are even!