The problem from the image you uploaded is:

Given $f(x) = 3x + a$ and $(f \circ f)(x) = 9x + a + 3$, you are asked to find the value of $f(a)$.

Let's break down the problem:

1. $f(x) = 3x + a$ — This is the original function.
2. $(f \circ f)(x)$ means applying $f$ to the result of $f(x)$. So first, we apply $f$ to $x$: $f(x) = 3x + a$ Applying $f$ again to the result: $f(f(x)) = f(3x + a)$ Substitute $3x + a$ into $f$: $f(3x + a) = 3(3x + a) + a = 9x + 3a + a$

We know $(f \circ f)(x) = 9x + a + 3$, so: $9x + 4a = 9x + a + 3$

Equating the coefficients: $4a = a + 3$ $3a = 3$ $a = 1$

Substituting $a = 1$ into $f(x)$: $f(x) = 3x + 1$

Now, we find $f(a)$: $f(a) = f(1) = 3(1) + 1 = 4$

So, $f(a) = 4$.

Answer: C. 4

Would you like more details or have any questions about the steps involved? Here are some additional topics you might find interesting:

1. How do function compositions work in general?
2. What happens if the coefficients of $x$ had been different?
3. How to solve for $x$ when $f(x) = g(x)$ for non-linear functions?
4. The concept of function inverses and their properties.
5. How to graph the composition of two functions.

Tip: When solving problems involving compositions of functions, always verify your final answers by substituting back into the original equations to ensure consistency.