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MHT CET20228 Aug 2022Morning ShiftMathematicsContinuity and DifferentiabilityActual

f(x)= array cc x-4 |x-4| +a, & for x 4 array . Is continuous at x=4 , then

Options

  1. Aa=0,b=0
  2. Ba=1,b=1
  3. Ca=-1,b=1
  4. Da=1,b=-1

Correct answer

D. a=1,b=-1

Step-by-step solution

For continuity at x=4 aligned & _ x 4⁻ f(x)=f(4)= _ x 4⁺ f(x) & _ x 4⁻ x-4 |x-4| +a=a+b= _ x 4⁺ x-4 |x-4| +b & -1+a=a+b=1+b & a=1 and b=-1 aligned

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