If $f\circ g = g\circ f$ then $f = g$?

Question

Is it true or there's an error in my understanding?

$$f\circ g = g\circ f \iff f=g?$$

Answer 1

Any pair of (integer) power functions have this property. $$(x^n)^m =(x^m)^n$$

Answer 2

Well:

$$f(x) = x, g(x) = x^2$$

Then

$$f(g) = x^2 = g(f)$$

Therefore, it is not true.