To solve the problem, we'll first calculate the functions $f(x)$ and $g(x)$ using the given expressions and then substitute the values as needed.

Given:

• $f(x) = 5x + 6$
• $g(x) = 9 - x^2$

(a) Calculate $f(g(0))$:

1. First, find $g(0)$: $g(0) = 9 - (0)^2 = 9 - 0 = 9$

2. Now, substitute $g(0) = 9$ into $f(x)$: $f(g(0)) = f(9) = 5(9) + 6 = 45 + 6 = 51$

So, $f(g(0)) = 51$.

(b) Calculate $g(f(0))$:

1. First, find $f(0)$: $f(0) = 5(0) + 6 = 0 + 6 = 6$

2. Now, substitute $f(0) = 6$ into $g(x)$: $g(f(0)) = g(6) = 9 - (6)^2 = 9 - 36 = -27$

So, $g(f(0)) = -27$.

Final Answers:

• $f(g(0)) = 51$
• $g(f(0)) = -27$

Do you have any questions or need more details?

Related Questions:

1. What is the value of $f(f(2))$?
2. Calculate $g(g(1))$.
3. What is the inverse function of $f(x) = 5x + 6$?
4. If $h(x) = f(x) + g(x)$, what is $h(1)$?
5. Determine the values of $x$ where $f(x) = g(x)$.

Tip:

When working with composite functions, always evaluate the inner function first before substituting into the outer function.