Question

For \[y=\sec^{-1}x\], which ranges contain the two separated branches?

Options

• \[[-\frac{\pi}{2},0)\] and \[(0,\frac{\pi}{2}]\]

• \[[0,\frac{\pi}{2})\] and \[(\frac{\pi}{2},\pi]\]

• \[[0,\pi]\] and \[[-\frac{\pi}{2},\frac{\pi}{2}]\]

• \[(-\frac{\pi}{2},\frac{\pi}{2})\] and \[(0,\pi)\]

Answer 1

The two branches of \[y=\sec^{-1}x\] are separated. One stays in \[[0,\frac{\pi}{2})\], while the other stays in \[(\frac{\pi}{2},\pi]\].