Question

Find domain of $\frac{1}{\sqrt{7-6x-x^2}}$

Answer 1

$y=\dfrac{1}{\sqrt{7-6x-x^{2}}$4

For existance of $y$,

$7-6x-x^2>0$

$\Rightarrow x^2+6x-7<0$

$\Rightarrow (x+7)(x-1)<0$

$\Rightarrow x\in (-7,1)$= Domain