Question

The number of integers in the domain of $\ln \left(\frac{\sqrt{x+2}-\sqrt{6-x}}{\sqrt{-x^2+4x+12}}\right)$ is

• A. 3
• B. 5
• C. 7
• D. 9

Answer 1

Answer: (A)

$\ln \left(\frac{1}{\sqrt{6-x}}-\frac{1}{\sqrt{x+2}}\right)$
$6-x>0$....(i)
$x+2>0$....(ii)
$(x+2)>6-x$
$2x>4$
$x>2$....(iii)
$x\in (2,6)$