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 answer
    B
    $0$
  • 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'.

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