Question

Find $gof$ and $fog$, if
(i) $f\left(x\right)=|x|$ and $g\left(x\right)=|5x-2|$
(ii) $f\left(x\right)=8x^3$ and $g\left(x\right)=x^{\frac{1}{3}}$

Answer 1

$\left(i\right)f\left(x\right)=|x|$ and $g\left(x\right)=|5x-2|$

$g\left(f\right(x\left)\right)=|5|x|-2|$ and $f\left(g\right(x\left)\right)=|5x-2|$
$\left(ii\right)f\left(x\right)=8x^3$ and $g\left(x\right)=x^{\frac{1}{3}}$

$f\left(g\right(x\left)\right)=f\left(x^{\frac{1}{3}}\right)=8$

$g\left(f\right(x\left)\right)=g\left(8x^3\right)=2$