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.

Explore how to evaluate composite functions using f(x) = 4x - 1. Learn step-by-step how to find f(4) and then use it to determine f(4f(4)). This problem covers key concepts in functions and linear equations. Suitable for Grades 7-9.

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