Show that if f (x) is an even function, then g ( f (x)) is even.
Given that f(x) is an even function, we know that f(-x) = f(x) for all x in the domain.
Let's consider g(f(x)):
g(f(x)) = g(f(-x)) (since f(x) is an even function)
= g(f(x)) (since f(-x) = f(x))
From the above, we can see that g(f(x)) = g(f(x)), which means g(f(x)) is an even function.
Therefore, if f(x) is an even function, then g(f(x)) is also an even function.