If `F :[1,oo)vec[2,oo)` is given by `f(x)=x+1/x ,t h e nf^(-1)(x)` equals. `(x+sqrt(x^2-4))/2` (b) `x/(1+x^2)` (c) `(x-sqrt(x^2-4))/2` (d)`1+sqrt(x^2-4)`

Explanation

`{Let} f(x)=x+frac{1}{x}=y`



`Rightarrow {x}={f}^{-1}({y}) {x}^{2}-{yx}+1=0`



Solving `x^{2}-y x+1`, we get



`x^{2}-y x+1=0`


`x=frac{y pm sqrt{y^{2}-4}}{2} `


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