If $ f(x)=-\frac{x|x|}{1+x^{2}} $, then $ f^{-1}(x) $ equals

JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

f(x)=-\frac{x|x|}{1+x^{2}}

, then

f^{-1}(x)

equals

View answer and explanation

Correct option: B

(\operatorname{sgn} x) \sqrt{\frac{|x|}{1-|x|}}

Option B (

(\operatorname{{sgn}} x) \sqrt{{\frac{{|x|}}{{1-|x|}}}}

) is correct because it represents the inverse function of the given function, considering the sign of x.

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