Given the functions $f(x) = x^3 + 5x$ and $g(x) = 2x + 1$, you want to find $f(g(1))$.

Here's how to solve it step by step:

1. Evaluate $g(1)$: $g(1) = 2(1) + 1 = 2 + 1 = 3$

2. Substitute $g(1)$ into $f(x)$: $f(g(1)) = f(3)$

3. Evaluate $f(3)$: $f(3) = 3^3 + 5(3) = 27 + 15 = 42$

So, $f(g(1)) = 42$.

Would you like more details or have any questions?

Here are five related questions you might find interesting:

1. How would you find $g(f(1))$ with the same functions?
2. What happens if you compose these functions in reverse order?
3. How do you differentiate $f(g(x))$ using the chain rule?
4. Can you graph $f(x)$ and $g(x)$ to visualize the composition?
5. What is the significance of the composition of functions in real-world applications?

Tip: When composing functions, always remember to evaluate the innermost function first before applying the outer function.