Question

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

• A. $[0,2]$
• B. $[0,2)$
• C. $[1,2)$
• D. $[1,2]$

Answer 1

The correct option is C $[1,2)$

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

For $f\left(x\right)$ to be defined $4-x^2\ge 0,-1\le 2-x\le 1$ and $2-x\ne 1$

$\Rightarrow$ $-2\le x\le 2$ and $-1\le 2-x\le 1$

$\Rightarrow$ $-2\le x\le 2$ and $-3\le -x\le -1$

$\Rightarrow$ $-2\le x\le 2$ and $1\le x\le 3$

$\therefore$ Domain of $f\left(x\right)=[1,2)$