For a suitably chosen real constant a, let a function, f : R –{– a}® R be defined by f (x) = a a – + x x . Further suppose that for any real number x ¹ – a and f (x) ¹ – a, ( fof ) (x) = x. Then 1 2 æ ö ç ÷ – è ø f is equal to:

Question:

For a suitably chosen real constant a, let a function, $f: \mathrm{R}-\{-\mathrm{a}\} \rightarrow \mathrm{R}$ be defined by $f(x)=\frac{\mathrm{a}-x}{\mathrm{a}+x}$. Further suppose that for any real number $x \neq-a$ and $f(x) \neq-a$, $(f \circ f)(x)=x$. Then $f\left(-\frac{1}{2}\right)$ is equal to:

  1. $\frac{1}{3}$

  2. $-\frac{1}{3}$

  3. $-3$

  4. 3


Correct Option: 4

JEE Main Previous Year 1 Question of JEE Main from Mathematics Sets, Relations and Functions chapter.
JEE Main Previous Year Sep. 06, 2020 (II)

Solution:

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