Question

Suppose that f is even and g is odd.
a. show that f o f is even
b. show that g of is even.

Answer 1

you are doing the same thing on previous problems
are you unsure what the o looking thing between f and f means?
it just means f(f(x)) in a
an for b you look at g(f(x))

I would do the same thing here
Let h(x)=f(f(x))
replace x with -x
and try to show h(-x)=h(x) since in a you want even result

Answer 2

You can show f is even.
f o f (-x) = f( f( -x) ) = f ( f (x) ) = f o f ( x)

Answer 3

g o f (-x) = g(f(-x)) = g( f(x)) = g o f (x)

therefore g o f is even