Thread: Functions

Let and be odd and even functions respectively. How can we construct an even function out of these?

Plenty of ways, but why can't you just take as the even function? What's the point of using in constructing an even function?

Edit: In case you mean you need to construct an even function from only , some simple ways would be to take the absolute value or square the function.





These would both be even functions.

What does "construct out of them" mean?

Originally Posted by drumist

Plenty of ways, but why can't you just take as the even function? What's the point of using in constructing an even function?

Edit: In case you mean you need to construct an even function from only , some simple ways would be to take the absolute value or square the function.





These would both be even functions.

And if you really have to use both functions, so would and .

Now, if the problem had been to construct an even function from two odd functions, that would have been a little more interesting!

Also their composition{ g(x) = f1(f2(x)) and h(x) = f2(f1(x)) } are even!