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

JEE MATHEMATICS MCQ: FUNCTIONS

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The range of

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

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Correct option: C

[0,2 \pi)

Option C (

[0,2 \pi)

) is correct because the range of the function is determined by the range of the arcsine function, which is limited to less than 1.

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

f(x)=x(4-x)

f^{-1}(x)

g(f(x))=|\sin x|

f(g(x))=(\sin \sqrt{x})^2

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

f\left( x \right) = x - \left[ x \right]

{f^{ - 1}}\left( x \right)

f: R \rightarrow R

f(x)=x^4

f(x)=(x+1)^2-1(x \geq-1)

S=\left\{x: f(x)=f^{-1}(x)\right\}