#### Answer

$f[g(x)]=\sqrt{8x^{2}-4}$
$g[f(x)]=8x+10$

#### Work Step by Step

In the expression for f(x), replace x with g(x)
$f[g(x)]=\sqrt{g(x)+2}$
$=\sqrt{(8x^{2}-6)+2}$
$=\sqrt{8x^{2}-4}$
In the expression for g(x), replace x with f(x)
$g[f(x)]=8(f(x))^{2}-6$
$=8(\sqrt{x+2})^{2}-6$
$=8x+16-6$
$=8x+10$