Question

Find the domain of \[\cos^{-1}(x^2-4)\].

Options

• \[(-\infty,-\sqrt{5}]\cup[\sqrt{5},\infty)\]

• \[[-\sqrt{3},\sqrt{3}]\]

• \[[-\sqrt{5},\sqrt{5}]\]

• \[[-\sqrt{5},-\sqrt{3}]\cup[\sqrt{3},\sqrt{5}]\]

Answer 1

From \[-1\leq x^2-4\leq1\], adding \[4\] gives \[3\leq x^2\leq5\]. Thus \[\sqrt{3}\leq|x|\leq\sqrt{5}\], producing the two stated intervals.