Problems with some work problems

[powp]

Hello

I am having problems with two problems can somebody help me??

1. Suppose g is a odd function and let h = f of g. Is h always an odd function? What if f is odd? what if f is even??

2. Express the sufrace area of a cube as a function of the length of a side.

thanks any help would be great

P

 

[hypermorphism]

Both problems are straightforward cases of applying the definitions.

 

[powp]

What do you mean by applying the definitions?

Thanks

 

[hypermorphism]

Write out the property that makes g an odd function in symbolic terms. See what it means with respect to h. Write out the property that f is an even/odd function. See what both mean with respect to h in symbolic terms by just plugging in all these definitions. Compare the behavior of h to the behavior of even and odd functions given in their definition.

 

[powp]

So if
f of g with f being an odd function would result in h = f(g(-x)) = f(-x) = -x so function h would be odd or -h(x) = h(-x)

and if was even it would result in h = f(g(-x)) = f(-x) = x so function h is even when f is even

Is this correct?

 

[hypermorphism]

So if
f of g with f being an odd function would result in h = f(g(-x)) = f(-x) ...

This line should read h = f(g(-x)) = f(-g(x)) if g is an odd function. We don't know that g(x)=-x, we just know that g(-x) = -g(x) if g is odd. If f is also an odd function, we get f(-g(x)) = -f(g(x)) = -h.

 

[powp]

thanks for the reply :)