Question

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

Options

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

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

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

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

Answer 1

For \[y=\sec^{-1}x\], inputs must satisfy \[x\leq-1\] or \[x\geq1\]. Its range / principal value is \[[0,\pi]\setminus\{\frac{\pi}{2}\}\].