Question

Find the domain of definition of the following function.
$y=\frac{\sqrt{3x-7}}{\sqrt[6]{6x+1}}.$

Answer 1

$y=\frac{\sqrt{3x-9}}{\sqrt[6]{6x+1}}$

$3x-7\ge 0$

$x+1>0$

$3x\ge \frac{7}{3}$

$x+1>0$

$x>-1$

So,the Domain of $y=[\frac{-7}{3},\infty )$