Question

Find the range of the following real valued functions
$\left(i\right)\log \left|4-x^2\right|$

$\left(ii\right)\frac{x^2-4}{x-2}$

Answer 1

Solution - Range of i) $log|4-x^2|$

Range of $4-x^2$ is $(-\infty ,4]$

then $|4-x^2|$ range is $[0,\infty ]$

then range of $log|4-x^2|$ is R.

ii) $\frac{x^2-4}{x-2}$ $x\ne 2$ then $\to x+2$

So range is $R-\{2+2\}$

$R-\left\{4\right\}$