Suppose $f(x)=x^{7}+9$ and $g(x)=\sqrt{x}$. Then \[ f(g(x))= \] help (formulas) $g(f(x))=$ help (formulas)

Step 1 ：Substitute \(g(x)\) into \(f(x)\) for \(f(g(x))\), so wherever we see an \(x\) in \(f(x)\), we replace it with \(g(x)\).

Step 2 ：So, \(f(g(x)) = (g(x))^{7} + 9 = (\sqrt{x})^{7} + 9 = x^{7/2} + 9\).

Step 3 ：Substitute \(f(x)\) into \(g(x)\) for \(g(f(x))\), so wherever we see an \(x\) in \(g(x)\), we replace it with \(f(x)\).

Step 4 ：So, \(g(f(x)) = \sqrt{f(x)} = \sqrt{x^{7} + 9}\).

Step 5 ：Therefore, \(f(g(x)) = x^{7/2} + 9\) and \(g(f(x)) = \sqrt{x^{7} + 9}\).

Step 6 ：Final Answer: \(\boxed{f(g(x)) = x^{7/2} + 9, g(f(x)) = \sqrt{x^{7} + 9}}\)