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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2017 · Mathematics · Continuity and Differentiability

Let g be the greatest integer function. Then the function...

Let gg be the greatest integer function. Then the function f(x)=(g(x))2−g(x)f(\mathrm{x})=(\mathrm{g}(\mathrm{x}))^2-\mathrm{g}(\mathrm{x}) is discontinuous at

Options

  1. Aall integers
  2. Ball integers except 0 and 1
  3. Call integers except 0
  4. Dall integers except 1

Correct answer

D. all integers except 1

Step-by-step solution

f(x)=(g(x))2−g(x)f(x)=(g(x))^2-g(x) Given, g(x)g(x) is greatest integer function. So, g(x)=[x]g(x)=[x]. ∴f(x)=[x]2−[x]f(x)\therefore f(x)=[x]^2-[x]f(x) is discontinuous at every integer except x=1x=1
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