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COMEDK2024MathematicsContinuity and Differentiability

If f(x)= array lc x^2+1 & x 0 x^3-a & 0 x 1 and it is continuous 2 b-x & x 1 array . x R , then

Options

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

Correct answer

C. a=-1 and b= 3 2

Step-by-step solution

If f(x) is continuous, then array lll f (0⁻ ) =f (0⁺ ) 0+1 =0-a -1 =a f (1⁻ ) =f (1⁺ ) 1-a =2 b-1 =2 b-1 3 2 =b array

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