Let f: R - \ 0, 1\ → R be a function such that f(x) + f((1)/(1 -...

Given,

$f\left(x\right) + f\left(\dfrac{1}{1 - x}\right) = 1 + x$

$x = 2 ⇒ f\left(2\right) + f\left(- 1\right) = 3 \ldots \left(1\right)$

$x = - 1 ⇒ f\left(- 1\right) + f$\left(\dfrac{1}{2}\right) = 0 \ldots \left(2\right)$</p><p>$x = \dfrac{1}{2} ⇒ f\left(\dfrac{1}{2}\right) + f\left(2\right) = \dfrac{3}{2} \ldots \left(3\right)$</p><p>On subtracting equation \left(3\right) and equation \left(2\right)$ we get,

$f ( 2 ) - f ( - 1 ) = \dfrac{3}{4} . . . . . . . . ( 4 )$

On adding equation \left(1\right)$and equation \left(4\right)$ we get,

$2f\left(2\right) = \dfrac{9}{2}$

$⇒ f\left(2\right) = \dfrac{9}{4}$