Match each function in List I with its range in List II.

Match each function in List I with its range…

Question 25

HardOriginal question

Match each function in List I with its range in List II.

List I	List II
A. $\sin^{-1} x$	I. $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
B. $\cos^{-1} x$	II. $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$
C. $\tan^{-1} x$	III. $(0, \pi)$
D. $\cot^{-1} x$	IV. $[0, \pi]$

A-II, B-IV, C-I, D-IIICorrect answerYour answerA-IV, B-II, C-I, D-IIICorrect answerYour answerA-II, B-IV, C-III, D-ICorrect answerYour answerA-IV, B-II, C-III, D-ICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$\sin^{-1}$ and $\tan^{-1}$ live around 0, closed and open; $\cos^{-1}$ and $\cot^{-1}$ live in $[0, \pi]$ , closed and open.
$\tan$ and $\cot$ blow up at the ends, so their ranges are open.

Concept: The four principal branches
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsDomains and ranges

Practise this chapter →

Ten questions from Inverse Trigonometric Functions, at your own pace.

Practise this chapter →

Ten questions from Inverse Trigonometric Functions, at your own pace.

Question 25

Explanation