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Question: Answered & Verified by Expert
Let $\mathrm{g}$ be the greatest integer function. Then the function $f(\mathrm{x})=(\mathrm{g}(\mathrm{x}))^{2}-\mathrm{g}(\mathrm{x})$ is discontinuous at
MathematicsContinuity and DifferentiabilityNDANDA 2017 (Phase 2)
Options:
  • A all integers
  • B all integers except 0 and 1
  • C all integers except 0
  • D all integers except 1
Solution:
1497 Upvotes Verified Answer
The correct answer is: all integers except 1
$\mathrm{f}(\mathrm{x})=(\mathrm{g}(\mathrm{x}))^{2}-\mathrm{g}(\mathrm{x})$
Given, $\mathrm{g}(\mathrm{x})$ is greatest integer function. So, $\mathrm{g}(\mathrm{x})=[\mathrm{x}]$. $\therefore \mathrm{f}(\mathrm{x})=[\mathrm{x}]^{2}-[\mathrm{x}]$
$\mathrm{f}(\mathrm{x})$ is discontinuous at every integer except $\mathrm{x}=1$

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