explain how many elements are in the range of (f of f)(x) if f(x) defines a constant function over (-infinity,infinity)

Question

I am unsure about how to properly solve this question

Answer 1

Because f(x) defines a constant function in (-infinity, infinity), f(x) = a (a is constant) for every x in (-infinity, infinity)

 

f(f(x)) = f(a)

 

And because of the definition of f(x) - f(x) = a (a is constant) for every x in (-infinity, infinity), we also have f(a)=a

 

So the number of elements are is the range of (f of f)(x) is 1. (a)