The range of f(x) = 4 sin⁻¹(x²... |JEE Main 2023

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JEE MAIN 2023

13-04-2023 S2

Question

The range of $f(x)=4 \sin ^{-1}\left(\frac{x^2}{x^2+1}\right)$

Select the correct option:

$[0, \pi]$

$[0,2 \pi)$

$[0, \pi)$

$[0,2 \pi]$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$$ \begin{aligned} & f(x)=4 \sin ^{-1}\left(\frac{x^2}{x^2+1}\right) \\ & \frac{x^2+1-1}{x^2+1}=1-\frac{1}{x^2+1} \Rightarrow[0,1) \end{aligned} $$ Range of $f(x)=[0,2 \pi)$

Question Tags

JEE Main

Mathematics

Easy

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