Mathematics

Problem

Define the function

f:\mathbb R\to\mathbb R

f(x)=\begin{cases}x+2,&x\le 0,\\x^{2},&x>0,\end{cases}

and let

g:\mathbb R\setminus\{1\}\to\mathbb R

be given by

g(x)=\dfrac{1}{1-x}

. Find the domain of the composition

g\circ f