Question

If $f:R\to R$ and $g:R\to R$ are given by $f\left(x\right)=|x|$ and $g\left(x\right)=\left[x\right]$ for each $x\in R,$ then $\{x\in R:g\left(f\left(x\right)\right)\le f\left(g\left(x\right)\right)\}=$

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

Answer 1

The correct option is D $R$

$g\left(f\left(x\right)\right)\le f\left(g\left(x\right)\right)\Rightarrow g\left(\left|x\right|\right)\le f\left(\left[x\right]\right)\Rightarrow \left[\left|x\right|\right]\le \left[\left|x\right|\right]$
This is true for each $x\in R$