We need to evaluate $f(h(4))$.

1. First, find $h(4)$: $h(x) = x + 1$ Substituting $x = 4$: $h(4) = 4 + 1 = 5$

2. Next, find $f(h(4)) = f(5)$: $f(x) = 2x + 1$ Substituting $x = 5$: $f(5) = 2(5) + 1 = 10 + 1 = 11$

Thus, $f(h(4)) = 11$.

Would you like more details on function composition or any other aspect? Here are five related questions for further practice:

1. If $g(x) = x^2 + 3$, what is $f(g(3))$?
2. What is $f(h(x))$ as a general expression?
3. If $f(x) = 3x - 2$, what is $f(h(4))$?
4. Can you solve for $f(f(2))$ given $f(x) = 2x + 1$?
5. If $h(x) = x - 1$, what is $f(h(7))$?

Tip: When solving composite functions, always start by evaluating the innermost function first.