Question

If $f:R\to R$ and $g:R\to R$ are given by f(x) = |x| and g(x) = [x], then $g\left(f\right(x\left)\right)\le f\left(g\right(x)$ is true for -

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

Answer 1

The correct option is D $R$

$g\left(f\right(x\left)\right)\le f\left(g\right(x\left)\right)\Rightarrow g\left(|x|\right)\le f\left[x\right]\Rightarrow \left[|x|\right]\le |\left[x\right]|$
This is true for $xϵR.$