Question

The domain of the function $f\left(x\right)=\frac{1}{\sqrt{4x-x^2}}+\sqrt{4-x^2}$ is

• A. $[0,4]$
• B. $[0,2]$
• C. $(0,2]$
• D. $(0,4)$

Answer 1

The correct option is C $(0,2]$

Given,

$f\left(x\right)=\frac{1}{\sqrt{4x-x^2}}+\sqrt{4-x^2}$

For function to be defined
$4x-x^2>0$and $4-x^2\ge 0$
$\Rightarrow 0<x<4$ and $-2\le x\le 2$
$\Rightarrow x\in (0,2]$
Hence, option 'C' is correct.