Question

The domain of the function $f(x)={\log }_{10}\frac{x-5}{x^2-10x+24}-3\sqrt{x+5}$ is

• A. $(-5,\infty )$
• B. $(5,\infty )$
• C. $(2,5)\cup (5,\infty )$
• D. $(4,5)\cup (6,\infty )$

Answer 1

Answer: (D)

$\frac{x-5}{x^2-10x+24}>0\text{ and }x+5>0$
$\Rightarrow x>5,x>6\Rightarrow x>6\Rightarrow x\in (6,\infty )$
$\text{ or }x<5,x>4\Rightarrow 4<x<5\Rightarrow x\in (4,5)$