18. If f(x) = 2x + 1 and h(x) = x + 1 what is f(h(4))

A. 9

B. 10

C. 11

D. 19

To solve \( f(h(4)) \), we need to follow these steps:

1. **First, find \( h(4) \):**

   \[
   h(x) = x + 1
   \]
   \[
   h(4) = 4 + 1 = 5
   \]

2. **Next, find \( f(h(4)) = f(5) \):**

   \[
   f(x) = 2x + 1
   \]
   \[
   f(5) = 2(5) + 1 = 10 + 1 = 11
   \]

So, the correct answer is **C. 11**.

Would you like any further explanation or have any questions? Here are five related questions to consider:

1. What is \( f(h(2)) \) given the same functions \( f(x) \) and \( h(x) \)?
2. If \( h(x) \) were \( h(x) = 2x \), what would \( f(h(4)) \) be?
3. How do you find the composition of two functions in general?
4. What is the inverse of \( f(x) = 2x + 1 \)?
5. How would the answer change if \( h(x) \) were a different linear function?

**Tip:** When dealing with function composition, always start by evaluating the innermost function first.

If f(x) = 2x + 1 and h(x) = x + 1, what is f(h(4))? A. 9, B. 10, C. 11, D. 19

Learn how to solve the function composition problem where f(x) = 2x + 1 and h(x) = x + 1, specifically f(h(4)). This detailed solution is suitable for students in Grades 9-10 and covers key concepts in algebra and function composition.

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