even, odd????

Question

If f and g are real-valued functions both with a real domain

(a) if f is even and g is odd, is f ○ g even odd or neither???
(b) if f is even and g is odd, is g ○ f even odd or neither???
(c) If f is even, can f ○ g be odd, how???

please help it makes no sense

Answer 1

f(x) is even if f(x) = f(-x) (like the cos(x))
g(x) is odd if g(x) = -g(-x) (like the sin(x))

Consider
f(g(-x)) = f(-g(x)) = f(g(x) ===> even
g(f(-x)) = g(f(x)) ===> even

Suppose f(x) = cos(x), which is even. Then if g(x) = Arccos(sin(x)), f ○ g = cos(Arccos(sin(x))) = sin(x), which is odd.