Maharashtra BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions2 Marks
Question
Find the domain of$\sec^{-1}(3\text{x}-1)$
✓
Answer
Domain of $\sec^{-1}\text{x}$ lies in the interval $(-\infty,-1]\cup[1,\infty)$
$\therefore$ Domain of $\sec^{-1}(3\text{x}-1)$ lies in the interval $(-\infty,-1]\cup[1,\infty)$
$\Rightarrow-\infty\leq3\text{x}-1\leq-1$ and $1\leq3\text{x}-1\leq\infty$
$\Rightarrow-\infty\leq3\text{x}\leq0$ and $2\leq3\text{x}\leq\infty$
$\Rightarrow-\infty\leq\text{x}\leq0$ and $\frac{2}{3}\leq\text{x}\leq\infty$
Domain of $\sec^{-1}\text{x}$ lies in the interval $(-\infty,0]\cup\Big[\frac{2}{3},\infty\Big).$
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