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WBJEE2023MathematicsContinuity and DifferentiabilityActual

Let (f(x)= array cc x+1, & -1 x 0 -x, & 0 x 1 array . )

Options

  1. A(f(x) ) is discontinuous in ([-1,1] ) and so has no maximum value or minimum value in ([-1,1] )
  2. B(f(x) ) is continuous in ([-1,1] ) and so has maximum value and minimum value
  3. C(f(x) ) is discontinuous in ([-1,1] ) but still has the maximum and minimum value
  4. D(f(x) ) is bounded in ([-1,1] ) and does not attain maximum or minimum value

Correct answer

C. (f(x) ) is discontinuous in ([-1,1] ) but still has the maximum and minimum value

Step-by-step solution

Hint : (f(x)= cases x+1 & -1 x 0 -x & 0 obviously (f(x) ) has local maximum at (x=0 )

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