A differentiable function f satisfies the relation f(x+1x−1)=2f(x)+3x−1 ∀ x∈R−{1}. If(i) the range of the function excludes the interval (a1,a2) on the real number line,(ii) relative maximum and minimum values of f(x) occur at x=b1 and x=b2,then the value of a21+a22+b21+b22 is

A differentiable function f satisfies the relation f(x+1x−1)=2f(x)+3

1.	A differentiable function f satisfies the relation f(x+1x−1)=2f(x)+3x−1 ∀ x∈R−{1}. If(i) the range of the function excludes the interval (a1,a2) on the real number line,(ii) relative maximum and minimum values of f(x) occur at x=b1 and x=b2,then the value of a21+a22+b21+b22 is
Answer» A differentiable function $f$ satisfies the relation $f (\frac{x + 1}{x - 1}) = 2 f (x) + \frac{3}{x - 1} \forall x \in R - {1} .$ If $(i)$ the range of the function excludes the interval $(a_{1}, a_{2})$ on the real number line, $(i i)$ relative maximum and minimum values of $f (x)$ occur at $x = b_{1}$ and $x = b_{2},$ then the value of $a_{1}^{2} + a_{2}^{2} + b_{1}^{2} + b_{2}^{2}$ is