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!