Question

Find the domain of the function:

$f\left(x\right)=\frac{1}{\sqrt{x^2-4x}}$.

Answer 1

The function will be defined if $x^2-4x>0$

or, $x(x-4)>0$

or, $x>0$ and $x>4$ or, $x<0$ and $x<4$

or, $x\in (4,\infty )$ or, $x\in (-\infty ,0)$.

Domain is $(-\infty ,0)\cup (4,\infty )$.