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.