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Let a function f : 1 , ∞ → 0 , ∞ be defined by f x = 1 - 1 x . Then f is

Options

  1. Ainjective but not surjective
  2. Bboth injective as well as surjective
  3. Cnot injective but it is surjective
  4. Dneither injective nor surjective

Correct answer

B. both injective as well as surjective

Step-by-step solution

f x = 1 - 1 x = x - 1 x = x - 1 x f ′ x = 1 x 2 f ′ x > 0 ∴ f x is injective and range of function is 0 , ∞ Hence, injective and surjective

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