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MHT CET202210 Aug 2022Morning ShiftMathematicsFunctionsActual

Let A= x R / x is not a positive integer). Let a function f be defined as f: A R so that f(x)= 2 x x-1 , then f is

Options

  1. ANot injective.
  2. Bsurjective but not injective.
  3. Cneither injective nor surjective.
  4. Dinjective but not surjective.

Correct answer

D. injective but not surjective.

Step-by-step solution

aligned & f(x)= 2 x x-1 & f^ (x)= (x-1) 2-2 x(1-0) (x-1)^2 = -2 (x-1)^2 <0 aligned f(x) is strictly decreasing so f(x) is injective But f(x)=4 2 x x-1 =4 x=2 (which is a positive integer) i.e., 4 R (co-domain of f ) has no pre-image in A (domain of f ) So, ' f ' is not surjective

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