CUET Preparation Today
Which of the following is the range of the principal value of $\sec ^{-1} x$. |
$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ $\left(0, \frac{\pi}{2}\right)$ $[0, \pi)$ $[0, \pi]-\left\{\frac{\pi}{2}\right\}$ |
$[0, \pi]-\left\{\frac{\pi}{2}\right\}$ |
The correct answer is Option (4) - $[0, \pi]-\left\{\frac{\pi}{2}\right\}$ $y=\sec^{-1}x.$ $\text{Principal value range of } \sec^{-1}x \text{ is defined so that sec }y \text{ is one–one}.$ $y\in[0,\pi],\;y\ne\frac{\pi}{2}.$ $\text{Correct option: }[0,\pi]-\left\{\frac{\pi}{2}\right\}.$ |
