Question

Find the domain of definition of the following function:
$f\left(x\right)=\frac{\sqrt{x^2-2x}}{{\log }_5(x-1)}.$

Answer 1

For

$\sqrt{x^2-2x}{x}^2-2x\ge 0x(x-2)\ge 0x\in (-\infty ,0]\cup [2,\infty )$

and

${\log }_5(x-1)x-1>0x\ne 2x>1$

Taking intersection, we get

$x\in (2,\infty )$