Question

Find the domain of \[\sec^{-1}(3x-1)\].

Options

• \[\left(-\infty,\frac{2}{3}\right]\]

• \[(-\infty,0]\cup\left[\frac{2}{3},\infty\right)\]

• \[\left[0,\frac{2}{3}\right]\]

• \[(-\infty,0)\cup\left(\frac{2}{3},\infty\right)\]

Answer 1

Solving \[3x-1\leq-1\] gives \[x\leq0\]. Solving \[3x-1\geq1\] gives \[x\geq\frac{2}{3}\], so the domain is their union.