To solve $ff(x)$ where $f(x) = 4x + 9$, we need to evaluate $f(f(x))$. Here's the step-by-step process:

1. $f(x) = 4x + 9$, so $f(f(x))$ means substituting $f(x)$ into itself: $f(f(x)) = f(4x + 9)$

2. To evaluate $f(4x + 9)$, substitute $4x + 9$ wherever $x$ appears in $f(x) = 4x + 9$: $f(4x + 9) = 4(4x + 9) + 9$

3. Expand the brackets: $f(4x + 9) = 16x + 36 + 9$

4. Simplify: $f(f(x)) = 16x + 45$

Final Answer:

$ff(x) = 16x + 45$

Would you like me to explain any part in more detail?

Related Questions:

1. What is $f^3(x)$ (applying $f$ three times)?
2. How do you solve $f(x) = 0$ for $x$?
3. How would $ff(x)$ change if $f(x) = 2x + 3$?
4. Can you calculate $g(f(x))$ if $g(x) = x^2$?
5. How do you find the inverse of $f(x) = 4x + 9$?

Tip:

When solving $f(f(x))$, carefully substitute and expand step by step to avoid mistakes!