Find gof and fog, if

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

(ii) $f(x) = 8{x^3}\;\;and\;\;g(x) = {x^{1/3}}.$

(i) $f(x) = \;|x|\;\;and\;\;g(x) = \;|5x - 2|$
$gof = g(f(x)) = g(|x|) = \;|5|x| - 2,$
$fog = f(g(x)) = f(|5x - 2|) = \;\parallel 5x - 2\parallel = |5x - 2|$

(ii) $f(x) = 8{x^3}\;\;and\;\;g(x) = {x^{1/3}}$

$gof = g[f(x)] = g(8{x^3}) = {(8{x^3})^{1/3}} = 2x$
and $fog = f(g(x)) = f({x^{1/3}}) = 8{({x^{1/3}})^3} = 8x.$