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KVPY2017MathematicsFunctions

Let R be the set of real numbers and f : R R be defined by f(x)= x 1+[x]² , where [x] is the greatest integer less than or equal to x , and x =x-[x] . Which of the following statements are true ? I. The range of f is a closed interval II. f is continuous on R . III. f is one-one on R .

Options

  1. AI only
  2. BII only
  3. CIII only
  4. DNone of I, II and III

Correct answer

D. None of I, II and III

Step-by-step solution

f(x)= x 1+[x]² f(x)= array cc x+1 2 ; & -1 x < 0 x ; & 0 x < 1 x-1 2 ; & 1 x < 2 x-2 5 ; & 2 x < 3 & & So - on array . Now check accordingly

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