Idempotency

I'm as confused as hell here anon
Show that a function f : A -> A is idempotent if and only if f(x) = x for every element of p(f), the range of f.

Does anyone know what the fuck this means?

Idempotent, in this case, means that f(f(x)) = f(x) for any x.

Assume f is idempotent.  Let x be an element of f(A) and let a be such that f(a) = x.  Since f is idempotent, f(x) = f(f(a)) = f(a) = x.

The converse is easy.

Seriously thats it? It seems so simple now

>>3
You're impotent.

>>4
Surjections lasting longer than four hours, though rare, require immediate medical attention.

>>5
That's a quality joke right there.

I dun care who u are, thats funny rite thar.