Let be defined by f(x)= 1-x 1+x^2

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let f:[1−2,1+2]→[−2+12,2+12]f:\left[1-\sqrt2,1+\sqrt2\right]\to\left[-\frac{\sqrt2+1}{2},\frac{\sqrt2+1}{2}\right] be defined by f(x)=1−x1+x2.f(x)=\frac{1-x}{1+x^2}. If f−1(x)={−1+λ4x−4x2+12x,x≠0,μ,x=0,f^{-1}(x)=\begin{cases}\dfrac{-1+\lambda\sqrt{4x-4x^2+1}}{2x},&x\ne0,\\\mu,&x=0,\end{cases} then λ+μ\lambda+\mu is

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