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We are given two functions:

\[
f(x) = -3x - 10
\]
\[
g(x) = 3x^2 - 6x - 12
\]

We are asked to find \( f(g(x)) \), which is the composition of the functions \( f \) and \( g \).

### Step 1: Substitute \( g(x) \) into \( f(x) \)

To find \( f(g(x)) \), we substitute the expression for \( g(x) \) into the function \( f \). This means we replace every occurrence of \( x \) in \( f(x) \) with \( g(x) \).

\[
f(g(x)) = -3(g(x)) - 10
\]

Substitute \( g(x) = 3x^2 - 6x - 12 \) into this expression:

\[
f(g(x)) = -3(3x^2 - 6x - 12) - 10
\]

### Step 2: Simplify

Now distribute the \(-3\) to each term inside the parentheses:

\[
f(g(x)) = -9x^2 + 18x + 36 - 10
\]

Combine the constants:

\[
f(g(x)) = -9x^2 + 18x + 26
\]

So, the composition \( f(g(x)) \) is:

\[
f(g(x)) = -9x^2 + 18x + 26
\]

### Final Answer:
\[
f(g(x)) = -9x^2 + 18x + 26
\]

Would you like further details or explanations? 

Here are five follow-up questions you might consider:
1. How do we graph the composition \( f(g(x)) \)?
2. What is the domain of \( f(g(x)) \)?
3. Can we find the inverse of the composed function \( f(g(x)) \)?
4. How would the result change if \( f(x) \) were a quadratic function?
5. What are the key points where \( f(g(x)) = 0 \)?

**Tip:** Always substitute carefully and simplify step-by-step to avoid errors in function composition.

Given the functions f(x) = -3x - 10 and g(x) = 3x^2 - 6x - 12, find f(g(x)).

Explore the steps to find the composition of the functions f(x) = -3x - 10 and g(x) = 3x^2 - 6x - 12. Learn how to substitute and simplify to find f(g(x)), which is a crucial concept in high school algebra.

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