The problem asks to find $f(g(x))$, where the functions are defined as:

$f(x) = 4 + 5x$ $g(x) = 2x - 1$

To find $f(g(x))$, substitute $g(x) = 2x - 1$ into $f(x)$:

$f(g(x)) = f(2x - 1)$

Now, replace $x$ in the function $f(x) = 4 + 5x$ with $2x - 1$:

$f(2x - 1) = 4 + 5(2x - 1)$

Simplify:

$f(2x - 1) = 4 + 5(2x) - 5(1)$ $f(2x - 1) = 4 + 10x - 5$ $f(2x - 1) = 10x - 1$

So, $f(g(x)) = 10x - 1$.

The correct answer is:

$\boxed{10x - 1}$.

Do you want further details or have any other questions?

Here are 5 related questions:

1. How do you evaluate composite functions in general?
2. What are the common mistakes in solving $f(g(x))$?
3. How do you interpret composite functions graphically?
4. Can composite functions be reversed? How?
5. What are real-world applications of composite functions?

Tip: Always ensure you substitute the inner function correctly when solving composite functions.