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MHT CET2010MathematicsContinuity and Differentiability

The value of a and b such that the function f(x)= array ll -2 x, & - x - 2 a x+b, & - 2 < x < 2 is continuous x, & 2 x array . in [- , ] , are

Options

  1. A-1,0
  2. B1,0
  3. C1,1
  4. D-1,1

Correct answer

D. -1,1

Step-by-step solution

For continuity in [- , ] , we must have array l At x=- 2 , f (- 2 )= _ x (- 2 )⁻ (-2 x) = _ x (- 2 )⁺ (a x+b) 2=-a+b array At x= 2 , f ( 2 )= _ x ( 2 )⁻ (a x+b)= _ x ( 2 )⁺ x 0=a+b On solving Eqs. (i) and (ii) we get, a=-1, b=1

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