We are asked to find the composition of functions $f(x) = x + 4$ and $g(x) = 4x + 4$ for different cases. Let's break them down:

Part (a): $(f \circ g)(x)$

This means we substitute $g(x)$ into $f(x)$.

1. $g(x) = 4x + 4$
2. Now substitute this into $f(x)$: $f(g(x)) = f(4x + 4) = (4x + 4) + 4$ Simplifying: $f(g(x)) = 4x + 8$

Thus, $(f \circ g)(x) = 4x + 8$.

Would you like me to solve the remaining parts (b), (c), and (d) as well? Let me know if you have any questions about this!

Related Questions:

1. What is the general method for composing two functions?
2. Can function composition be commutative? Why or why not?
3. How do we handle compositions of functions where inputs are constants instead of variables?
4. What are the applications of function composition in real-world scenarios?
5. Can you explain how the chain rule in calculus is related to function composition?

Tip:

Always verify your results by checking the individual steps, especially when substituting functions into one another.