To solve for $f(4f(4))$ given the function $f(x) = 4x - 1$, follow these steps:

Step 1: Find $f(4)$

Substitute $x = 4$ into the function: $f(4) = 4(4) - 1 = 16 - 1 = 15$

Step 2: Find $f(4f(4))$

Now, substitute $f(4) = 15$ into the function $f(x)$: $f(4f(4)) = f(4 \times 15) = f(60)$

Step 3: Find $f(60)$

Substitute $x = 60$ into the function: $f(60) = 4(60) - 1 = 240 - 1 = 239$

Thus, $f(4f(4)) = 239$.

Would you like more details or have any questions? Here are five related questions to consider:

1. What is the general method for evaluating composite functions?
2. How do you determine the inverse of the function $f(x) = 4x - 1$?
3. What happens to the function if the coefficient of $x$ changes?
4. How does the slope of a linear function affect its graph?
5. How can you solve $f(x) = 0$ for this function?

Tip: Always perform operations step by step, especially with composite functions, to avoid mistakes.