Consider the functions $f(x)=x^{3}-5$ and $g(x)=\sqrt[3]{x+5}$. (a) Find $f(g(x))$. (b) Find $g(f(x))$. (c) Determine whether the functions $f$ and $g$ are inverses of each other. (a) What is $f(g(x))$ ? $f(g(x))=\square$ (Simplify your answer.) Give any values of $x$ that need to be excluded from $f(g(x))$. Select the correct choice below and fill in any answer boxes within your choice. A. $x \neq$ (Use a comma to separate answers as needed.) B. No values should be excluded from the domain. (b) What is $g(f(x))$ ? $g(f(x))=\square$ (Simplify your answer.) Give any values of $x$ that need to be excluded from $g(f(x))$. Select the correct choice below and fill in any answer boxes within your choice. A. (Use a comma to separate answers as needed.) B. No values should be excluded from the domain. (c) Are the functions $f$ and $g$ inverses of each other? Choose the correct answer below. No Yes

Step 1 ：Given the functions $f(x)=x^{3}-5$ and $g(x)=\sqrt[3]{x+5}$, we can find $f(g(x))$ by substituting $g(x)$ into $f(x)$.

Step 2 ：So, $f(g(x))=(\sqrt[3]{x+5})^{3}-5$.

Step 3 ：Simplifying this gives $f(g(x))=x+5-5$.

Step 4 ：So, $f(g(x))=\boxed{x}$.

Step 5 ：There are no values that need to be excluded from $f(g(x))$, so the answer is B. No values should be excluded from the domain.

Step 6 ：Next, we find $g(f(x))$ by substituting $f(x)$ into $g(x)$.

Step 7 ：So, $g(f(x))=\sqrt[3]{(x^{3}-5)+5}$.

Step 8 ：Simplifying this gives $g(f(x))=\sqrt[3]{x^{3}}$.

Step 9 ：So, $g(f(x))=\boxed{x}$.

Step 10 ：There are no values that need to be excluded from $g(f(x))$, so the answer is B. No values should be excluded from the domain.

Step 11 ：Finally, we determine whether the functions $f$ and $g$ are inverses of each other.

Step 12 ：Since $f(g(x))=x$ and $g(f(x))=x$, the functions $f$ and $g$ are inverses of each other.

Step 13 ：So, the answer is Yes, the functions $f$ and $g$ are inverses of each other.