Question

Find the range of \[f(x)=\cos^{-1}(1-x^2)\] on its domain.

Options

• \[\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\]

• \[[0,\pi]\]

• \[\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\]

• \[(0,\pi)\]

Answer 1

For \[x\in[-\sqrt{2},\sqrt{2}]\], the quantity \[1-x^2\] covers \[[-1,1]\]. Since \[\cos^{-1}([-1,1])=[0,\pi]\], the range is \[[0,\pi]\].