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AP EAMCET202418 May 2024Morning ShiftMathematicsContinuity and DifferentiabilityActual

f(x)= array cc (2 x^2-a x+1 )- (a x^2+3 b x+2 ) x+1 & ; if x -1 k & , if x=-1 array . is a real valued function. If a, b, k R and f is continuous on R then k=

Options

  1. A- 1 3
  2. B6
  3. Ca-2
  4. Da-3

Correct answer

D. a-3

Step-by-step solution

Given the function f(x)= array cc (2 x^2-a x+1 )- (a x^2+3 b x+2 ) x+1 & if x -1 k & if x=1 array . Now, _ x -1 (2-a) x^2-(a+3 b) x-1 x+1 For existence of limit 2-a+a+3 b-1=0 b=- 1 3 Now, _ x -1 (2-a) x^2-(a-1) x-1 x+1 aligned & = _ x -1 2 x(2-a)-(a-1) 1 & = -2(2-a)-a+1 1 =-4+a+1=a-3 aligned Since, f(x) is continuous at x=-1 So, k=a-3

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