The function h(x)=1 /x+9 can be expressed in the form f(g(x)), where g(x)=(x+9), and f(x) is defined as: f(x) =

To express the function \( h(x) = \frac{1}{x+9} \) in the form \( f(g(x)) \), where \( g(x) = x+9 \), we need to determine the function \( f(x) \).

We know that \( g(x) = x + 9 \), so when we substitute this into \( h(x) \), we get:

\[
h(x) = \frac{1}{g(x)}
\]

This means that \( f(x) = \frac{1}{x} \), since we are applying the function \( f \) to \( g(x) \) to get \( h(x) \).

Therefore, \( f(x) = \frac{1}{x} \).

### Summary:
\[
h(x) = f(g(x)) = \frac{1}{g(x)}, \text{ where } f(x) = \frac{1}{x} \text{ and } g(x) = x + 9
\]

Do you want more details, or have any questions?

---

Here are 5 related questions to expand this concept:
1. How would the composition change if \( g(x) = x - 9 \)?
2. What happens if \( f(x) = x^2 \)? How does that affect \( h(x) \)?
3. Can the composition \( f(g(x)) \) be used to represent more complex functions?
4. How do you decompose a function into compositions of two functions in general?
5. What is the derivative of \( h(x) \) in terms of \( f(x) \) and \( g(x) \)?

**Tip:** Function composition can simplify the analysis of more complex expressions, breaking them into smaller, more manageable parts!

The function h(x) = 1 / (x + 9) can be expressed in the form f(g(x)), where g(x) = (x + 9), and f(x) is defined as: f(x) = ?

Learn how to express the function h(x) = 1 / (x + 9) using function composition. Explore algebraic concepts such as identifying f(x) and g(x) in a composed function. Suitable for 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