Question

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

Options

• \[[-\sqrt{2},\sqrt{2}]\]

• \[[-1,1]\]

• \[(-\infty,-\sqrt{2}]\cup[\sqrt{2},\infty)\]

• \[\mathbb{R}\]

Answer 1

For definition, \[-1\leq1-x^2\leq1\] is required. This becomes \[0\leq x^2\leq2\], hence \[-\sqrt{2}\leq x\leq\sqrt{2}\].