Let f (x) = (x + 2)2 – 2, x ≥ – 2, then f -1(x) is equal to(a) \ – InterviewSolution

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1.

Let f (x) = (x + 2)2 – 2, x ≥ – 2, then f -1(x) is equal to(a) \(- \sqrt{2+x}\) - 2(b) \( \sqrt{2+x} +2\)(c) \( \sqrt{2+x} -2\)(d) \(- \sqrt{2+x}+2\)

Answer»

Answer : (c) \( \sqrt{2+x}-2\)

Let y = f (x) = (x + 2)² – 2

⇒ y + 2 = (x + 2)²

⇒ x + 2 = \(\sqrt{y+2}\)

⇒ x = \(\sqrt{y+2}\) - 2

⇒ f^-1 (x) = \( \sqrt{2+x}-2\)

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