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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

f(x) is differentiable function satisfying the relationship f^2(x) + f^2(y) + 2(xy-1) = f^2(x+y) x, y R Also f(x) > 0 x R and f( 2 ) = 2 . Then which of the following statement(s) is/are correct about f(x) ?

Options

  1. A[f(3)] = 3 ( [ ] denotes greatest integer function)
  2. Bf( 7 ) = 3
  3. Cf(x) is even
  4. Df'(0) = 0

Correct answer

A. [f(3)] = 3 ( [ ] denotes greatest integer function)

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