Question

# If f: [1,∞)→[2,∞) is given by f(x)=x+1x  , then f−1(x) is equal tox+√x2−42x1+x2x−√x2−421+√x−4

Solution

## The correct option is A x+√x2−42f(x)=x+1x, for f−1(x) Put f (x) = y ∴y=x2+1x or x2 - xy + 1 = 0 ⇒x=y±√y2−42 ∴f−1(y)=y+√y2−42     (neglect - ve, as x > 1) ∴f−1(x)=x+√x2−42

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