Match the LIST-I with LIST-II
| LIST-I | LIST-II | ||
| Function | Range (Principal value) | ||
| A. | \( \tan^{-1}x \) | I. | \( [0,\pi]-\left\{\displaystyle\frac{\pi}{2}\right\} \) |
| B. | \( \sec^{-1}x \) | II. | \( \left[-\displaystyle\frac{\pi}{2},\frac{\pi}{2}\right] \) |
| C. | \( \mathrm{cosec}^{-1}x \) | III. | \( \left[-\displaystyle\frac{\pi}{2},\frac{\pi}{2}\right]-\{0\} \) |
| D. | \( \sin^{-1}x \) | IV. | \( \left(-\displaystyle\frac{\pi}{2},\frac{\pi}{2}\right) \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-IV, B-I, C-III, D-II
(A) \( \tan^{-1}x \)
This matches (IV). tan takes every real value on the open interval \( \left(-\frac{\pi}{2},\frac{\pi}{2}\right) \); the end points are excluded because tan is not defined there.
(B) \( \sec^{-1}x \)
This matches (I). The principal branch is \( [0,\pi] \) without \( \frac{\pi}{2} \), where sec is not defined.
(C) \( \mathrm{cosec}^{-1}x \)
This matches (III). The principal branch is \( \left[-\frac{\pi}{2},\frac{\pi}{2}\right] \) without 0, where cosec is not defined.
(D) \( \sin^{-1}x \)
This matches (II). The principal branch is the closed interval \( \left[-\frac{\pi}{2},\frac{\pi}{2}\right] \).
So the matching is A-IV, B-I, C-III, D-II.
NCERT (2026-27 edition):
Basic Concepts
