Question

What are the domain and range / principal value of \[y=\cos^{-1}x\]?

Options

• Domain \[[-1,1]\]; range / principal value \[[0,\pi]\]

• Domain \[[-1,1]\]; range / principal value \[[-\frac{\pi}{2},\frac{\pi}{2}]\]

• Domain \[\mathbb{R}\]; range / principal value \[(0,\pi)\]

• Domain \[(-\infty,-1]\cup[1,\infty)\]; range / principal value \[[0,\pi]\setminus\{\frac{\pi}{2}\}\]

Answer 1

The domain of \[y=\cos^{-1}x\] is \[[-1,1]\]. Its range / principal value extends from \[0\] to \[\pi\], inclusive.