Q101 / 160 · AP EAMCET 2023 (16 May Shift 2) · Mathematics

Let $[\mathrm{t}]$ represents the greatest integer not more than $\mathrm{t}$.Then the number of discontinuous points of $f(x)$$=\left[X^{\frac{1}{x}}\right]$in $(0, \infty)$ is

  • A
    $0$
  • Correct answer
    B
    $1$
  • C
    $2$
  • D
    $\infty$

Solution

Given $f(x)=\left[x^{\frac{1}{x}}\right]$ Now for discontinuous point $x^{\frac{1}{x}}=\text { integer }$ $\Rightarrow x^{\frac{1}{x}}=$ integer only 1 possible so $f(x)=\left[x^{\frac{1}{x}}\right]$ is discontinuous at only one point.

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

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