Q41 / 125 · BITSAT 2020 · Mathematics

Let $[x]$ denote the greatest integer $\leq x$. If $f(x)=$ $[\mathrm{x}]$ and $g(x)=|x|,$ then the value of $\mathrm{f}\left(\mathrm{g}\left(\frac{8}{5}\right)\right)-\mathrm{g}\left(\mathrm{f}\left(-\frac{8}{5}\right)\right)$ is

  • A
    2
  • B
    -2
  • C
    1
  • Correct answer
    D
    -1

Solution

$\begin{aligned} &\text { Given that, } f(x)=[x] \text { and } g(x)=|x|\\ &\text { Now, } \mathrm{f}\left(\mathrm{g}\left(\frac{8}{5}\right)\right)=\mathrm{g}\left(\frac{8}{5}\right)=\left[\frac{8}{5}\right]=1 \end{aligned}$ and $\mathrm{g}\left(\mathrm{f}\left(-\frac{8}{5}\right)\right)=\mathrm{g}\left(\left[-\frac{8}{5}\right]\right)=\mathrm{g}(-2)=|-2|=2$ $\therefore \mathrm{f}\left(\mathrm{g}\left(\frac{8}{5}\right)\right)-\mathrm{g}\left(\mathrm{f}\left(-\frac{8}{5}\right)\right)=1-2=-1$

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

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