Q241 / 270 · NDA 2017 (Phase 2) · Mathematics

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

  • A
    all integers
  • B
    all integers except 0 and 1
  • C
    all integers except 0
  • Correct answer
    D
    all integers except 1

Solution

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

Hence, the correct answer is option: 'D'.

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