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MHT CET202415 May 2024Morning ShiftMathematicsFunctionsActual

Let f :[-1,3] R be defined as cases |x|+[x], & -1 x 1 x+|x|, & 1 x 2 x+[x], & 2 x 3 cases where [t] denotes the greatest integer function. Then f is discontinuous at

Options

  1. Aonly two points
  2. Bonly three points
  3. Cfour or more points
  4. Donly one point

Correct answer

B. only three points

Step-by-step solution

aligned & f (x)= array cc |x|+[x], & -1 x 1 x+|x|, & 1 x 2 x+[x], & 2 x 3 array . & f (x)= array cc -(x+1), & -1 x 0 x, & 0 x 1 2 x, & 1 x 2 x+2, & 2 x 3 x+3, & x=3 array . aligned f (x) is discontinuous at x=0,1,3 .

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