Question

Find the domain for $f\left(x\right)=\sqrt{{\log }_{0.4}\left(\frac{x-1}{x+5}\right)}$

• A. $(1,\infty )$
• B. $(-\infty ,-1)$
• C. $(2,\infty )$
• D. $(-\infty ,-2)$

Answer 1

The correct option is A $(1,\infty )$

$\sqrt{{\log }_{0.4}\left(\frac{x-1}{x+5}\right)}$ is defined for ${\log }_{0.4}\left(\frac{x-1}{x+5}\right)>0$

${\log }_{0.4}\left(\frac{x-1}{x+5}\right)$ is defined for

$\frac{x-1}{x+5}>0$ and $x+5\ne 0$

$\Rightarrow x\in (-\infty ,-5)\cap (1,\infty )$ and $x\ne -5$

$\Rightarrow x\in (1,\infty )$