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NDA2016MathematicsContinuity and DifferentiabilityActual

Paragraph: Let f(x)=[x] , where [.] is the greatest integer function and g(x)= x be two real valued functions over R . Question: Which of the following statements is correct?

Options

  1. ABoth f(x) and g(x) are continuous at x=0 .
  2. Bf(x) is continuous at x=0 , but g(x) is not continuous at x=0 .
  3. Cg(x) is continuous at x=0 , but f(x) is not continuous at x=0 .
  4. DBoth f ( x ) and g ( x ) are discontinuous at x =0 .

Correct answer

C. g(x) is continuous at x=0 , but f(x) is not continuous at x=0 .

Step-by-step solution

aligned & f(x)=[x] and g(x)= x & _ x 0⁺ f(x)=[0+h]=0 & _ x 0⁻ f(x)=[0-h]=-1 & f(0)=0 aligned f(x) is not continuous at x=0 and also g(x) is continuous at x=0 . (every trignometric function is continuous).

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