Question

how can one compute f o f as they are both functions from the same set?

Answer 1

What exactly is the question in particular? What you're asking is too vague.

Answer 2

If f is for example a function from the reals to reals then there is no problem. The outer f takes as its domain the range of the first f which is a subset of the reals.

Answer 3

Suppose\[
f:S\mapsto T
\]If\[
S\supseteq T
\]Then \[
f\circ f:S\mapsto T
\]Otherwise the outer function will receive inputs outside of its domain.

Answer 4

would fof = f^2?

Answer 5

\[
(f\circ f)(x) = f(f(x))
\]

Answer 6

You have to be more specific with the question because I don't quite get it.