https://file.aiquickdraw.com/mathbot/file/1727392137035aa4lx4f4.jpg

Let's solve the problem step by step. We are given two functions:

- \( f(x) = 2x - 9 \)
- \( g(x) = 4 - x^2 \)

We are asked to calculate:

1. \( f(g(0)) \)
2. \( g(f(0)) \)

### (a) Calculating \( f(g(0)) \):
First, calculate \( g(0) \):
\[
g(0) = 4 - (0)^2 = 4
\]
Now, substitute \( g(0) = 4 \) into \( f(x) \):
\[
f(4) = 2(4) - 9 = 8 - 9 = -1
\]
So, \( f(g(0)) = -1 \).

### (b) Calculating \( g(f(0)) \):
First, calculate \( f(0) \):
\[
f(0) = 2(0) - 9 = -9
\]
Now, substitute \( f(0) = -9 \) into \( g(x) \):
\[
g(-9) = 4 - (-9)^2 = 4 - 81 = -77
\]
So, \( g(f(0)) = -77 \).

### Final Answers:
- \( f(g(0)) = -1 \)
- \( g(f(0)) = -77 \)

Let me know if you'd like more details or have any other questions! Here are 5 related questions for further practice:

1. What is \( f(g(2)) \)?
2. If \( f(x) = 2x - 9 \), what is the inverse function \( f^{-1}(x) \)?
3. What is the value of \( g(1) \)?
4. Find \( g(f(1)) \).
5. Solve for \( x \) when \( f(x) = 0 \).

**Tip**: When solving compositions of functions, always work from the innermost function outward.

Given that f(x) = 2x - 9 and g(x) = 4 - x^2, calculate (a) f(g(0)) = (b) g(f(0)) =

Learn how to solve a composition of functions problem where f(x) = 2x - 9 and g(x) = 4 - x^2. This problem demonstrates how to calculate f(g(0)) and g(f(0)) using substitution and evaluation of functions. Suitable for students in Grades 10-12.

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