Question

Find the range of the following functions
$\frac{1}{x-5}$

Answer 1

$f\left(x\right)=\frac{1}{x-5}$

Let, $y=\frac{1}{x-5}$

$⟹1=y(x-5)$

$⟹1=xy-5y$

$⟹xy=1+5y$

$⟹x=\frac{1+5y}{y}$

$⟹f^{-1}\left(y\right)=\frac{1+5y}{y}$

$\therefore f^{-1}\left(x\right)=\frac{1+5x}{x}$

$Range=R-\left\{0\right\}$