Even & Odd Functions: What Happens When Applied?

[Firepanda]

If i had an even fuction and i applied another even function to it, would the end result still be even?

Other questions follow the same pattern, if i had an odd function and applied another odd function to it, would it still be odd?

And suppose i had an even function and applied an odd function to it, what would it be then?

I suppose the first question is true, the next two i had simply no idea, I can't tell what would happen to functions with many terms in if i spplied other functions to it. I'm not after to prove it, because I'm aweful at that :P But something to help me figure out the answer to these questions would be very helpful!

Thanks

 

[Dick]

A function is even if f(-x)=f(x) and odd if f(-x)=-f(x). Write the composition as f(g(x)). Use whatever the rules are for f and g to compare f(g(-x)) to f(g(x)).