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

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

Steps

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: $\boxed{f(g(x)) = x^{7/2} + 9, g(f(x)) = \sqrt{x^{7} + 9}}$