Let f : R → R be defined as f (x) = x2 + 1. Then find f –1(– 5)( – InterviewSolution

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Let f : R → R be defined as f (x) = x2 + 1. Then find f –1(– 5)(a) {0} (b) ϕ (c) {5} (d) {– 5, 5}

Answer»

Answer: (b) = ϕ

f (x) = x²+ 1

Let y = f (x) = x² + 1

⇒ y – 1 = x²

⇒ x = ± \(\sqrt{y-1}\)

⇒ f^–1(x) = ± \(\sqrt{x-1}\)

∴ f^–1(– 5) = ± \(\sqrt{-5-1}\) ± \(\sqrt{-6}\) ∉ R

∴ f^–1(– 5) is the null set.

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