Q43 / 160 · TS EAMCET 2007 · Mathematics
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
- A$x$
- Correct answerB$0$
- C$f(x)$
- D$g(x)$
Solution
Given, $f(x)=x-[x], g(x)=[x]$ for $x \in R$.
$\begin{aligned} \therefore \quad f(g(x)) & =f([x]) \\ & =[x]-[x] \\ & =0\end{aligned}$
Hence, the correct answer is option: 'B'.