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KVPY2010MathematicsContinuity and Differentiability

Let f : R R be a continuous function satisfying f ( x )= x + ₀^ x f ( t ) dt , for all x R . Then the number of elements in the set S = x R ; f ( x )=0 is-

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

A. 1

Step-by-step solution

f ^ ( x )=1+ f ( x ) f ( x )= e ^ x -1 f ( x )=0 e ^ x =1 x =0 One solution

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