Find the domain and range of $y=\cos^{-1}\sqrt{1-x}$.
Can someone please help me with question above, as to how it's done? Thanks.
I am unfamiliar with what you do when there is a square root.
[Math] Find the domain and range of $y=\cos^{-1} \sqrt{1-x}$
functionsinversetrigonometry
Best Answer
Domain is $$0\leq x\leq 1$$ and range is $$0\leq y \leq \frac{\pi}{2}$$
As $cos^{-1}$x operates in $[-1,1]$ hence the argument must be between these hence the domain $0\leq x\leq 1$ also since domain is $[0,1]$ hence the range $0\leq y \leq \frac{\pi}{2}$.
$**Note**$: If you can determine the domain of a continous function between two intervals then plugging in the extreme values in the function provide you with the range.
Don't know of any exceptions yet.