Suppose

f:R ightarrow R

is a function from the set of real numbers to the same set with

f(x)=x+1 .

We write f^{2}

to represent f \circ f

and f^{n+1}=f^n \circ f .

Is it true that f^2 \circ f = f \circ f^2 ?

Why?

Is the set { g:R ightarrow R l g \circ f=f \circ g } infinite? Why?