Question

Let $f$, $g:R\to R$ be two functions defined as $f\left(x\right)=\left|x\right|+x$, $g\left(x\right)=\left|x\right|-x,\forall x\in R$. Then, find $fog\left(x\right)$

• A. $||x|-x|-|x|-x$
• B. $||x|-x|+|x|-x$
• C. $||x|-x|-|x|+x$
• D. None of thesse

Answer 1

Answer: (B)

$||x|-x|+|x|-x$

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

$g\left(x\right)=\left|x\right|-x$

$fog\left(x\right)=f\left(g\left(x\right)\right)$

$=f\left(\left|x\right|-x\right)$

$=\left|\left|x\right|-x\right|+\left|x\right|-x$