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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Let f(x) be a continuous function in [-1, 1] such that f(x) = cases (ax^2+bx+c) x^2 & ; -1 x < 0 1 & ; x = 0 (e^ x^2 -1) x^2 & ; 0 < x 1 cases Then which of the following is/are correct ?

Options

  1. Aa+b+c = 0
  2. Bb = a+c
  3. Cc = 1+b
  4. Db^2+c^2 = 1

Correct answer

C. c = 1+b

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