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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. Af(2) = e^4
  2. Bf(2) = 2e^2
  3. Cf(1) < 4
  4. Df(3) > 729

Correct answer

A. f(2) = e^4

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