Answer
$f[g(x)]=36x+72-22\sqrt{x+2}$
$g[f(x)]=2\sqrt{9x^{2}-11x+2}$
Work Step by Step
In the expression for f(x), replace x with g(x)
$f[g(x)]=9(g(x))^{2}-11g(x)$
$=9(2\sqrt{x+2})^{2}-11(2\sqrt{x+2})$
$=9[4(x+2)]-22\sqrt{x+2}$
$=36(x+2)-22\sqrt{x+2}$
$=36x+72-22\sqrt{x+2}$
In the expression for g(x), replace x with f(x)
$g[f(x)]=2\sqrt{f(x)+2}$
$=2\sqrt{(9x^{2}-11x)+2}$
$=2\sqrt{9x^{2}-11x+2}$
