Mathematics

Problem

Let

f:\mathbb R\to\mathbb R

be defined by

f(x)=ax+b

and let

g:\mathbb R\to\mathbb R

be defined by

g(x)=x^{2}

, where

a,b\in\mathbb R

. Find all ordered pairs

(a,b)

for which

g\circ f=f\circ g

as functions on

\mathbb R