Find the domain and range of the following functions. g(x)=x+4 x-… - Vidyadip

Question

Find the domain and range of the following functions.

$\mathrm{g}(\mathrm{x})=\frac{x+4}{x-2}$

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Answer

$g(x)=\frac{x+4}{x-2}$
Function $\mathrm{g}$ is defined everywhere except at $\mathrm{x}=2$.
$\therefore$ Domain of $\mathrm{g}=\mathrm{R}-\{2\}$
Let $y=g(x)=\frac{x+4}{x-2}$
$\therefore(x-2) y=x+4$
$\therefore \mathrm{x}(\mathrm{y}-1)=4+2 \mathrm{y}$
$\therefore$ For every $y$, we can find $\mathrm{x}$, except for $y=1$.
$\therefore y=1 \notin$ range of function $g$
$\therefore$ Range of $g=R-\{1\}$

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