If f(x) = 2x + 1 and h(x) = x + 1, what is f(h(4))?

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.

Learn how to solve the composite function f(h(4)) where f(x) = 2x + 1 and h(x) = x + 1. This problem involves evaluating functions and understanding function composition, suitable for students in Grades 6-8.

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