https://file.aiquickdraw.com/mathbot/file/1726725725178vuo08v21.jpg

We are given the functions:

\[
f(x) = 7x + 9 \quad \text{and} \quad g(x) = 2 - x^2
\]

Now, we need to compute the following:

### (a) \( f(g(0)) \)
1. First, calculate \( g(0) \):
   \[
   g(0) = 2 - (0)^2 = 2
   \]
2. Next, substitute \( g(0) = 2 \) into the function \( f(x) \):
   \[
   f(g(0)) = f(2) = 7(2) + 9 = 14 + 9 = 23
   \]
   So, \( f(g(0)) = 23 \).

### (b) \( g(f(0)) \)
1. First, calculate \( f(0) \):
   \[
   f(0) = 7(0) + 9 = 9
   \]
2. Now, substitute \( f(0) = 9 \) into the function \( g(x) \):
   \[
   g(f(0)) = g(9) = 2 - (9)^2 = 2 - 81 = -79
   \]
   So, \( g(f(0)) = -79 \).

### Final answers:
- \( f(g(0)) = 23 \)
- \( g(f(0)) = -79 \)

Would you like further details or have any questions about this process?

Here are 5 related questions to practice:
1. Find \( f(g(1)) \).
2. Find \( g(f(1)) \).
3. If \( h(x) = x^2 + 3x \), what is \( h(f(2)) \)?
4. What is the derivative of \( f(x) = 7x + 9 \)?
5. Solve for \( x \) if \( g(x) = 0 \).

**Tip:** When working with composite functions like \( f(g(x)) \), always evaluate the inner function first and then substitute its result into the outer function.

Given that f(x) = 7x + 9 and g(x) = 2 - x^2, calculate (a) f(g(0)) and (b) g(f(0)).

Learn how to calculate composite functions f(g(0)) and g(f(0)) where f(x) = 7x + 9 and g(x) = 2 - x^2. This problem covers key algebraic concepts related to functions and their compositions, suitable for Grades 9-12.

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