Question

For \[\sec^{-1}(3x-1)\], which condition on \[3x-1\] is required?

Options

• \[3x-1\leq-1\quad\text{or}\quad3x-1\geq1\]

• \[0<3x-1<\pi\]

• \[-1\leq3x-1\leq1\]

• \[3x-1\geq0\]

Answer 1

The input \[u\] of \[\sec^{-1}(u)\] must satisfy \[|u|\geq1\]. Therefore \[u\leq-1\] or \[u\geq1\], with \[u=3x-1\].