Question

Find the range of the following function given by
$\left(i\right)f\left(x\right)=\frac{3}{2-x^2}$
$\left(ii\right)f\left(x\right)=1-\left|x-2\right|$

Answer 1

Range of $i)$ $\frac{3}{2-x^2}$ Range is $R$ because when

$x^2\to 2^{+}f\left(x\right)=-\infty 2x^2\to -2f\left(x\right)=\infty$

$ii)$ $f\left(x\right)=1-|x-2|$

$1-$ positive

Range is $(-\infty ,1]$