Question

The domain of $f\left(x\right)=\sqrt{\frac{x+7}{x+5}}$ is

• A. $(-\infty ,-7]\cup (-5,\infty )$
• B. $(5,7)$
• C. $(-5,\infty )$
• D. $(-7,-5)\cup (5,7)$

Answer 1

The correct option is A $(-\infty ,-7]\cup (-5,\infty )$

$f$ is defined when $\frac{x+7}{x+5}\ge 0$ & $x+5\ne 0$ i.e. $x\ne -5$
$\frac{(x+5)(x+7)}{(x+5{)}^2}\ge 0$
$\Rightarrow (x+5)(x+7)\ge 0$
$\Rightarrow x\in (-\infty ,-7]\cup [-5,\infty )$
As $f$ is not defined at -5
$x\in (-\infty ,-7]\cup (-5,\infty )$