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Question: If \(f(x) = x^{2} + 1,\) then \(f^{- 1}(17)\) and \(f^{- 1}( - 3)\) will be...

If f(x)=x2+1,f(x) = x^{2} + 1, then f−1(17)f^{- 1}(17) and f−1(−3)f^{- 1}( - 3) will be

A

4, 1

B

4, 0

C

3, 2

D

None of these

Answer

3, 2

Explanation

Solution

Let y=x2+1y = x^{2} + 1⇒ x=±y−1x = \pm \sqrt{y - 1}

⇒ f−1(y)=±y−1f^{- 1}(y) = \pm \sqrt{y - 1} ⇒ f−1(x)=±x−1f^{- 1}(x) = \pm \sqrt{x - 1}

⇒ f−1(17)=±17−1=±4f^{- 1}(17) = \pm \sqrt{17 - 1} = \pm 4

and f−1(−3)=±−3−1=±−4f^{- 1}( - 3) = \pm \sqrt{- 3 - 1} = \pm \sqrt{- 4}, which is not possible.