QJEEM19Ma90ab: JEE Main 2019 Mathematics - Class 11 JEEM19Ma90ab Solution: If the function ƒ : R – {1, –1} A defined by ƒ(x) = , is…

Question

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If the function ƒ : R – {1, –1}

\to

A defined by
ƒ(x) =

{{{x^2}} \over {1 - {x^2}}}

, is surjective, then A is equal to

Accepted Answer

Let ƒ(x) =

{{{x^2}} \over {1 - {x^2}}}

= y

\Rightarrow

y\left( {1 - {x^2}} \right) = {x^2}

\Rightarrow

{x^2} = {y \over {1 + y}}

As

{x^2}

is always

\ge

0.

\therefore

{y \over {1 + y}}

\ge

0

y

\in

\left( { - \infty , - 1} \right) \cup \left[ {0,\left. \infty \right)} \right.

For surjective function co-domain = Range

\therefore

A is R – [–1, 0).

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