Question

If $f\left(x\right)=\frac{1}{\sqrt{x-5}}$, then find the domain and range of $f\left(x\right)$.

Answer 1

Consider the problem

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

For $f\left(x\right)$ to be define

$\begin{array}{c}x-5>0\\ \Rightarrow x>5\end{array}$

So, Domain of $f\left(x\right)$ is $\left(5,\infty \right)$

$\because \sqrt{x-5}>0$

So, Range of $f\left(x\right)$ is $\left(0,\infty \right)$