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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Let f be a differentiable function satisfying f'(x) = f'(-x) x R . Then

Options

  1. AIf f(1) = f(2) , then f(-1) = f(-2)
  2. B1 2 f(x) + 1 2 f(y) = f ( 1 2 (x + y) ) for all real values of x, y
  3. CLet f(x) be an even function, then f(x) = 0 x R
  4. Df(x) + f(-x) = 2f(0) x R

Correct answer

A. If f(1) = f(2) , then f(-1) = f(-2)

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