Question

The domain of the function f(x)=$\frac{\sqrt{-{\log }_{0.3}(x-1)}}{\sqrt{-x^2+2x+8}}$ is

• A. $(1,4)$
• B. $(2,4)$
• C. $[2,4)$
• D. none of these

Answer 1

Answer: (C)

$[2,4)$

Given,

f(x)=$\frac{\sqrt{-{\log }_{0.3}(x-1)}}{\sqrt{-x^2+2x+8}}$

For given function to be defined,
$-{\log }_{0.3}(x-1)\ge 0\Rightarrow {\log }_{10/3}(x-1)\ge 0\Rightarrow x-1\ge 1\Rightarrow x\ge 2$

and,

$-x^2+2x+8>0\Rightarrow x^2-2x-8<0\Rightarrow (x+2)(x-4)<0\Rightarrow -2<x<4$

Combining above two we get required domain $[2,4)$