If f: R rightarrow R and g: R rightarrow R ar | vedclass

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(B) Given,$f(x) = x - [x]$ and $g(x) = [x]$ for $x \in R$. We need to find the value of $f(g(x))$. By substituting $g(x)$ into $f(x)$,we get: $f(g(x))

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(B) Given,$f(x) = x - [x]$ and $g(x) = [x]$ for $x \in R$. We need to find the value of $f(g(x))$. By substituting $g(x)$ into $f(x)$,we get: $f(g(x)) = f([x])$. Since $f(x) = x - [x]$,substituting $[x]$ for $x$ gives: $f([x]) = [x] - [[x]]$. Since $[x]$ is an integer,the greatest integer function of an integer is the integer itself,i.e.,$[[x]] = [x]$. Therefore,$f([x]) = [x] - [x] = 0$. Thus,for every $x \in R, f(g(x)) = 0$.

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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