To find $f(g(1))$, we first need to evaluate $g(1)$ and then use this result as the input for $f(x)$.

Given the functions:

$f(x) = x^3 + 5x$ $g(x) = 2x + 1$

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

2. Substitute $g(1)$ into $f(x)$ to find $f(g(1))$: $f(g(1)) = f(3)$ Now, calculate $f(3)$: $f(3) = 3^3 + 5(3) = 27 + 15 = 42$

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

Would you like more details or have any questions?

Here are 5 related questions:

1. What is $f(g(x))$ in general terms?
2. How do you find the derivative of $f(x)$ or $g(x)$?
3. Can you determine the inverse function of $f(x)$ or $g(x)$?
4. What would be the value of $f(g(-1))$?
5. How does the composition of functions change if $g(x)$ was a quadratic function?

Tip: When working with compositions of functions, always start by evaluating the innermost function.