Question

The domain of the function $f\left(x\right)=\frac{1}{\sqrt{x-5}}$ is ___

• A. $[5,\infty ]$
• B. R${}^{+}$
• C. R
• D. $(5,\infty ]$

Answer 1

The correct option is D $(5,\infty ]$

$\text{Given,}f\left(x\right)=\frac{1}{\sqrt{x-5}}$
The domain of the real valued function is the set of values where the function is define. So the denominator should be real and not equal to zero.
$\therefore \sqrt{x-5}\ne 0\text{and}x-5>0$
$\Rightarrow x\ne 5\text{and}x>5$
Hence, the domain = (5, $\infty$]