Let X be a set (possibly infinite) and let f: X--->X. Define a function g: X--->X by requiring that g(x) = f(f(x)) for all x ϵ X.
a.) Prove that Range g(x) ⊆ Range f(x). Give an example where Range g(x) != Range f(x), using a set X with just three elements.
So i'm not really sure what this is asking... am I supposed to come up with my own function like f(x) = g(x) and f(g(x) = g(x)
or am I supposed to make my own function like f(x) = x and g(x) = 3x etc.
Any tips please?