The function is defined by h(x)= cases x+3,&-2 x 0, ^ 2 ,&0<x 3

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

The function

h:\mathbb{R}\to\mathbb{R}

is defined by

\displaystyle h(x)=\begin{cases}x+3,&-2\le x\le 0,\\x^{2},&0<x\le 3.\end{cases}

Find: (a) all real numbers

x

such that

h(x)=3

(b) whether

4

has a preimage under

h

, and if so, list all such

x