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` `1+sqrt(x^2-4)`

Explanation

Correct option is A)

Let` f(x)`=`x+1/x​=y`

`⇒x=f^(−1)y & x^2−yx+1=0`

Solving `x^2−yx+1`, we get
`x^2−yx+1=0`

`x=(y±sqrt(y^2−4))/2`

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`∴f^(−1)=(y±sqrt(y^2−4))/2`
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