Question

If $f\left(x\right)=|x|+2$ then range of $f\left(f\right(x\left)\right)$ is

• A. $(-\infty ,4)$
• B. $[4,\infty )$
• C. $[-4,4]$
• D. $noneofthese$

Answer 1

The correct option is B $[4,\infty )$

$f\left(x\right)=|x|+2$

$f\left(f\right(x\left)\right)=||x|+2|+2$

$\text{Here,}x\in R$

$0\le |x|<\infty$

$2\le |x|+2<\infty$

$2\le ||x|+2|<\infty$

$4\le ||x|+2|+2<\infty$

$\text{Hence,}{R}_f=[4,\infty )$