Let be defined by

MATHEMATICS · Numerical · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

f:[1-\sqrt{2},1+\sqrt{2}]\rightarrow\left[-\frac{\sqrt{2}+1}{2},\frac{\sqrt{2}+1}{2}\right]

be defined by

f(x)=\frac{1-x}{1+x^2}

. If

f^{-1}(x)=\begin{cases}\frac{-1+\lambda\sqrt{4x-4x^2+1}}{2x},&x\ne0,\\ \mu,&x=0,\end{cases}

then find

\lambda+\mu