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Let $\mathrm{f}(\mathrm{x})$ be the greatest integer function and $\mathrm{g}(\mathrm{x})$ be the modulus function.
What is $(\mathrm{f} \circ \mathrm{f})\left(-\frac{9}{5}\right)+(\mathrm{g} \circ \mathrm{g})(-2)$ equal to?
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What is $(\mathrm{f} \circ \mathrm{f})\left(-\frac{9}{5}\right)+(\mathrm{g} \circ \mathrm{g})(-2)$ equal to?
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$f(x) \rightarrow$ greatest integer function
$f(x)=[x]$
$g(x) \rightarrow$ modulus function $g(x)=|x|$
$f o f(x)=f(f(x))=f([x])$
$\begin{array}{l}\text { fof }\left(-\frac{9}{5}\right)=f(-2) \quad \because\left[-\frac{9}{5}\right]=-2 \\ =[-2]=-2 & \\ \operatorname{gog}(x)=g(|x|) & \\ =|| x|| & |x| \\ \quad=|x| & \\ \operatorname{gog}(-2)=|-2|=2 & \\ (\text { fof })\left(-\frac{9}{5}\right)+\operatorname{gog}(-2)=-2+2=0\end{array}$
$f(x)=[x]$
$g(x) \rightarrow$ modulus function $g(x)=|x|$
$f o f(x)=f(f(x))=f([x])$
$\begin{array}{l}\text { fof }\left(-\frac{9}{5}\right)=f(-2) \quad \because\left[-\frac{9}{5}\right]=-2 \\ =[-2]=-2 & \\ \operatorname{gog}(x)=g(|x|) & \\ =|| x|| & |x| \\ \quad=|x| & \\ \operatorname{gog}(-2)=|-2|=2 & \\ (\text { fof })\left(-\frac{9}{5}\right)+\operatorname{gog}(-2)=-2+2=0\end{array}$
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