https://file.aiquickdraw.com/mathbot/file/1725939219613c9suill2.jpg

To express the given function \( h(x) = (x + 2)^2 \) in the form \( h(x) = f(g(x)) \), we need to find appropriate functions \( f(x) \) and \( g(x) \).

### Step 1: Identify the Inner Function \( g(x) \)
Since the function inside the square is \( x + 2 \), we can choose:
\[
g(x) = x + 2
\]

### Step 2: Identify the Outer Function \( f(x) \)
Now, \( h(x) \) is obtained by squaring \( g(x) \). So, the outer function \( f(x) \) should be the squaring function:
\[
f(x) = x^2
\]

### Step 3: Express \( h(x) \) in the Form \( f(g(x)) \)
Substituting \( g(x) = x + 2 \) and \( f(x) = x^2 \) into the form \( f(g(x)) \), we have:
\[
h(x) = f(g(x)) = (g(x))^2 = (x + 2)^2
\]

Thus, the functions are:
\[
\{f(x), g(x)\} = \{x^2, x + 2\}
\]

Would you like more details or have any questions about this problem?

---

Here are 5 related questions you might find interesting:
1. How would the functions \( f(x) \) and \( g(x) \) change if \( h(x) = (x - 3)^3 \)?
2. Can you express \( h(x) = \sin(x + 1) \) in the form \( h(x) = f(g(x)) \)?
3. What are the functions \( f(x) \) and \( g(x) \) if \( h(x) = \sqrt{x - 4} \)?
4. How can you express \( h(x) = e^{2x} \) in the form \( f(g(x)) \)?
5. How would you express a polynomial like \( h(x) = (2x + 5)^4 \) using \( f(x) \) and \( g(x) \)?

**Tip:** When breaking down a composite function into \( f(g(x)) \), always start by identifying the innermost transformation (which becomes \( g(x) \)) and then determine the outer function \( f(x) \) accordingly.

Find functions f(x) and g(x) so the given function can be expressed as h(x) = f(g(x)). Use non-identity functions for f(x) and g(x). h(x) = (x + 2)^2.

Learn how to express the quadratic function h(x) = (x + 2)^2 as a composition of two non-identity functions f(x) and g(x). This problem demonstrates function composition with algebraic transformations, suitable for high school students in grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation