Question

Find the domain of ${\cos }^{-1}\left[\sqrt{\frac{1+x}{2}}\right]$

• A. $[-1,1]$
• B. $[0,1]$
• C. $\left[0.2\right]$
• D. None of these

Answer 1

Answer: (A)

$[-1,1]$

For given function to exist

$0⩽\sqrt{\frac{1+x}{2}}⩽1$

$\Rightarrow 0⩽\frac{1+x}{2}⩽1$

$\Rightarrow 0⩽1+x⩽2$

$\Rightarrow -1⩽x⩽1$

Therefore Domain of the given function is $\left[-1,1\right]$