If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$, where $[x]$ is the greatest integer not exceeding $x$, then for every $x \in R, f(g(x))$ is equal to

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Given, $f(x)=x-[x], g(x)=[x]$ for $x \in R$. $\begin{aligned} 	herefore \quad f(g(x)) & =f([x]) \ & =[x]-[x] \ & =0\end{aligned}$

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$,…

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