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KVPY2014MathematicsContinuity and Differentiability

For a real number x let [x] denote the largest number less than or equal to x . for x R let f(x)=[x] x . Then:

Options

  1. Af is differentiable on R
  2. Bf is symmetric about the line x=0
  3. C_ -3 ³ f(x) d x=0
  4. DFor each real , the equation f(x)- =0 has infinitely many roots.

Correct answer

D. For each real , the equation f(x)- =0 has infinitely many roots.

Step-by-step solution

f(x)=[x] x

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