CBSE Class 12 Mathematics 2023: question 21

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Step-by-step solution

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1. $\tan x$ restricted to $\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ is one-one and onto $\mathbb{R}$. So its inverse ${\tan }^{-1}x$ is defined for every real $x$.

   Domain of $f(x)={\tan }^{-1}x$ is $\mathbb{R}$ (all real numbers).

   1 mark

2. Range (principal value branch) of ${\tan }^{-1}x$ is $\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$. The end points are excluded because $\tan x$ is not defined at $\pm \frac{\pi }{2}$.

   1 mark

Answer: Domain = $\mathbb{R}$; Range = $\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$

Revise the chapter

• Chapter: Inverse Trigonometric Functions (notes, formulas, where marks are lost and every past question)
• Topic: Domain and Range of Inverse Trigonometric Functions