given that f(x) = 6x+6 and g (x) = 4 -x^2 , calculate  a:  f(g(0)) and  b: g(f(0))

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!

Given that f(x) = 6x + 6 and g(x) = 4 - x^2, calculate a: f(g(0)) and b: g(f(0))

Explore how to solve function compositions using f(x) = 6x + 6 and g(x) = 4 - x^2. Learn the step-by-step process to calculate f(g(0)) and g(f(0)) with clear explanations of the formulas and operations involved. Perfect for Grades 9-11 students.

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