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