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MHT CET20228 Aug 2022Evening ShiftMathematicsContinuity and DifferentiabilityActual

Let f: R R be a function defined as f(x)= array ccc 5 & , & if x 1 a+b x & , & if 1 < x < 3 b+5 x & , & if 3 x < 5 30 & , & if x 5 array then f . is

Options

  1. Acontinuous if a=5 and b=5 .
  2. Bcontinuous if a=-5 and b=10 .
  3. Cnot continuous for any values of a and b .
  4. Dcontinuous is a=0 and b=5 .

Correct answer

C. not continuous for any values of a and b .

Step-by-step solution

for continuity at x=1, a+b=5 for continuity at x=3, a+3 b=b+15 a+2 b=15 system of equation (i), (ii) and (iii) is inconsistent Hence, f(x) is not continuous for any values of a and b on R

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