Q93 / 160 · AP EAMCET 2003 · Mathematics

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are given by $f(x)=|x|$ and $g(x)=[x]$ for each $x \in R$, then $\{x \in R: g(f(x)) \leq f(g(x))\}$ is equal to

  • A
    $Z \cup(-\infty, 0)$
  • B
    $(-\infty, 0)$
  • C
    $Z$
  • Correct answer
    D
    $R$

Solution

We have, $f(x)=|x| \text { and } g(x)=[x]$ Now, $\quad g(f(x)) \leq f(g(x))$ $\Rightarrow \quad g(|x|) \leq f([x])$ $\therefore \quad[|x|] \leq|[x]| \forall x \in R$

Hence, the correct answer is option: 'D'.

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