Define the function by f(x)= cases x+2,&x 0, ^ 2 ,&x>0

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Define the function

f:\mathbb R\to\mathbb R

by

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

.

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