Discrete Math: Functions with Powers

[finalsblow]

Did this as a homework problem, got it wrong obviously. Not too sure how to solve it otherwise

Homework Statement

Let f be a function from A to A. Prove that for all m,n ε N, f^m*f^n = f^(m+N)

Homework Equations

The Attempt at a Solution

f^(m+1) f^(n+1) = f(f^m) * f(f^n)
= f(f^m * f^n) <--- this I think is what I did wrong
= f(f^(m+n)) since a^m * a^n = a^(m+n)
= f^(m+n+1)
= f^(x+1) where x = m+n

 

[finalsblow]

Can't find edit button:
Found an error.. it should say
1. Homework Statement
Let f be a function from A to A. Prove that for all m,n ε N, f^m*f^n = f^(m+n)