Assertion (A): The curve y = tan^-1 x never meets the line y = π/2. Reason (R): The range of tan^-1 x is the open interval (-π/2, π/2).

Question 71

MediumOriginal question

Assertion (A): The curve $y = \tan^{-1} x$ never meets the line $y = \frac{\pi}{2}$ .
Reason (R): The range of $\tan^{-1} x$ is the open interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

A is true: the graph gets ever closer to $y = \frac{\pi}{2}$ as $x$ grows.
R is true and explains A: $\frac{\pi}{2}$ is not a value of $\tan^{-1}$ .

Concept: Asymptotes of the graph of $\tan^{-1}$
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsGraphs of the inverse functions

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

Assertion (A): The curve y=tan⁡−1xy = \tan^{-1} xy=tan−1x never meets the line y=π2y = \frac{\pi}{2}y=2π​.Reason (R): The range of tan⁡−1x\tan^{-1} xtan−1x is the open interval (−π2,π2)\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)(−2π​,2π​).

Explanation

Assertion (A): The curve $y = \tan^{-1} x$ never meets the line $y = \frac{\pi}{2}$ .
Reason (R): The range of $\tan^{-1} x$ is the open interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ .