Given the functions \( f(x) = x^2 + 5x + 6 \) and \( h(x) = x + 2 \), we need to find \((h \circ f)(4)\).

### Step 1: Compute \( f(4) \)
\[
f(4) = 4^2 + 5(4) + 6
\]
\[
f(4) = 16 + 20 + 6 = 42
\]

### Step 2: Compute \( h(f(4)) = h(42) \)
\[
h(42) = 42 + 2 = 44
\]

### Final Answer:
\[
(h \circ f)(4) = 44
\]

Would you like more details on how this was calculated or have any questions?

### Related Questions:
1. How do you find the composition of two functions in general?
2. What are the properties of function composition?
3. Can the order of function composition affect the result?
4. How do you interpret the graph of a composed function?
5. How do you find the domain of a composed function?
6. What happens if one function is not defined at the output of the other?
7. How can you compose more than two functions?
8. How do you differentiate composed functions (Chain Rule)?

**Tip:** When composing functions, always evaluate the inner function first before substituting into the outer function.

Learn how to calculate the composition of functions (h ∘ f)(4) using f(x) = x² + 5x + 6 and h(x) = x + 2. Follow a step-by-step solution to find the value of (h ∘ f)(4). This problem involves function composition and quadratic equations, suitable for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation