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MHT CET202122 Sep 2021Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let f(x) cases =|x|+3, & if x -3 =-2 x, & if -3 < x < 3, then =6 x+2, & if x 3 cases

Options

  1. Af(x) is discontinuous at both x=-3 as well as x=3
  2. Bf(x) is continuous at x=-3 but discontinuous at x=3
  3. Cf(x) is continuous at x=-3 as well as x=3
  4. Df(x) of discontinuous at x-3 but f(x) is continuous at x=3

Correct answer

B. f(x) is continuous at x=-3 but discontinuous at x=3

Step-by-step solution

We have f(x)=-x+3 , if x -3 aligned & =-2 x , if -3 < x < 3 & =6 x +2 , if x 3 & x 3⁻ f(x) =-(-3)+3=6 and x 3⁺ f(x) =-2(-3)=6 and f(-3) & =-(-3)+3=6 & aligned Thus f ( x ) is continuous at x =-3 x 3⁻ f(x) =-2(3)=-6 and x 3⁺ f(x) =6(3)+2=20 Thus f ( x ) is not continuous at x =3 .

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