To find $f(g(0))$, we need to first evaluate $g(0)$ and then substitute that result into the function $f(x)$.

Step 1: Find $g(0)$

The function $g(x)$ is given as: $g(x) = -3x - 3$ Substitute $x = 0$: $g(0) = -3(0) - 3 = -3$

Step 2: Substitute $g(0)$ into $f(x)$

Now, substitute $g(0) = -3$ into the function $f(x)$. The function $f(x)$ is: $f(x) = 2x^2 - 5x + 12$ Substitute $x = -3$: $f(-3) = 2(-3)^2 - 5(-3) + 12$ Now, simplify the expression: $f(-3) = 2(9) + 15 + 12 = 18 + 15 + 12 = 45$

Thus, $f(g(0)) = 45$.

Final Answer:

$f(g(0)) = 45$

Would you like more details on any part of the solution?

Here are 5 questions related to this:

1. What happens if the function $g(x)$ changes?
2. How would the answer differ if $f(x)$ were linear instead of quadratic?
3. What are other techniques for combining functions?
4. How do you graph the composition of two functions?
5. How does changing the variable in one function affect the composition?

Tip: When composing functions, always solve the inner function first before plugging the result into the outer function.