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To solve for \( f(g(x)) \) using the given functions:

1. \( f(x) = 4x + 3 \)
2. \( g(x) = x - 7 \)

### Step-by-Step Solution:

1. We need to substitute \( g(x) \) into \( f(x) \). In other words, substitute \( g(x) = x - 7 \) into \( f(x) = 4x + 3 \).
   
2. Since \( f(x) = 4x + 3 \), replacing \( x \) with \( g(x) = x - 7 \), we get:
   \[
   f(g(x)) = 4(g(x)) + 3 = 4(x - 7) + 3
   \]

3. Now distribute the 4 to both terms inside the parentheses:
   \[
   f(g(x)) = 4x - 28 + 3
   \]

4. Combine like terms:
   \[
   f(g(x)) = 4x - 25
   \]

### Final Answer:

\[
f(g(x)) = 4x - 25
\]

Thus, the missing values in the equation \( f(g(x)) = ? x + \boxed{} \) are:

- The coefficient of \( x \) is **4**.
- The constant term is **-25**.

Would you like a deeper explanation on any part of this?

### Related Questions:

1. What is the general process for composing two functions?
2. How do you determine if two functions are inverses of each other?
3. How would you find \( g(f(x)) \) for the same functions?
4. Can you describe the domain and range of \( f(g(x)) \)?
5. What happens to \( f(g(x)) \) if we change \( f(x) \) or \( g(x) \)?

### Tip:
Always double-check your substitutions in function compositions to ensure accuracy when simplifying expressions!

Using the following equations, find f(g(x)): f(x) = 4x + 3, g(x) = x - 7

Learn how to solve the function composition problem f(g(x)) where f(x) = 4x + 3 and g(x) = x - 7. Step-by-step solution provided for Grades 8-10 students. Key algebra concepts covered include function composition and simplification.

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