Given the functions $f(x) = 6x + 6$ and $g(x) = 4 - x^2$, we will calculate the following:

a) $f(g(0))$

To solve $f(g(0))$, we need to follow these steps:

1. Find $g(0)$: $g(0) = 4 - (0)^2 = 4 - 0 = 4$
2. Substitute $g(0) = 4$ into $f(x)$: $f(4) = 6(4) + 6 = 24 + 6 = 30$ Thus, $f(g(0)) = 30$.

b) $g(f(0))$

To solve $g(f(0))$, we need to follow these steps:

1. Find $f(0)$: $f(0) = 6(0) + 6 = 0 + 6 = 6$
2. Substitute $f(0) = 6$ into $g(x)$: $g(6) = 4 - (6)^2 = 4 - 36 = -32$ Thus, $g(f(0)) = -32$.

Final answers:

• $f(g(0)) = 30$
• $g(f(0)) = -32$

Would you like more details on these calculations?

Here are 5 related questions:

1. What is the composition of two functions?
2. How do you calculate $f(g(x))$ for any general $x$?
3. Can you explain how to graph $f(x) = 6x + 6$ and $g(x) = 4 - x^2$?
4. How would you find the inverse of $f(x)$?
5. What are the domain and range of the function $g(x) = 4 - x^2$?

Tip: Always evaluate the inner function first when dealing with compositions of functions!