If function f,:,R - ,{ 1, - 1} to A defined by f,(x), = frac{{{x^2}}}{{1 - {

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1.Relation and Function

hard

If the function $f\,:\,R - \,\{ 1, - 1\} \to A$ defined by $f\,(x)\, = \frac{{{x^2}}}{{1 - {x^2}}},$ is surjective, then $A$ is equal to

A

$R\, - \,[ - 1,0)$

B

$R\, - \,( - 1,0)$

C

$R\, - \,\{ - 1\} $

D

$[0,\infty )$

(JEE MAIN-2019)

Solution

$y\, = \frac{{{x^2}}}{{1 – {x^2}}}$

Range of $y : R – [ – 1,0)$ for surjective function, $A$ must be same as above range.

Standard 12

Mathematics

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