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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Let f : R R be a continuous and differentiable function such that f(x+y) = f(x) f(y) x, y , f(x) 0 and f(0) = 1 and f'(0) = 2 . Let g(xy) = g(x) g(y) x, y and g'(1) = 2; g(1) 0 Identify the correct option :

Options

  1. Ag(2) = 2
  2. Bg(3) = 3
  3. Cg(3) = 9
  4. Dg(3) = 6

Correct answer

C. g(3) = 9

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