The function h(x)= 1/x-8 can be expressed in the form f(g(x)) where g(x)=x−8 and f(x) is defined as:

f(x)=

The function \( h(x) = \frac{1}{x-8} \) can be expressed in the form \( f(g(x)) \) where \( g(x) = x - 8 \).

To express \( h(x) \) in the form \( f(g(x)) \), let's follow these steps:

1. We are given \( g(x) = x - 8 \).
2. Then, substituting \( g(x) \) into \( h(x) \), we have \( h(x) = \frac{1}{g(x)} \).

Thus, we can express \( h(x) \) as:
\[ h(x) = f(g(x)) \]
where \( f(x) = \frac{1}{x} \).

So, the function \( f(x) \) is defined as:
\[ f(x) = \frac{1}{x} \]

Would you like further details or have any questions?

Here are 5 related questions:
1. How can you verify that \( h(x) = f(g(x)) \) for the given functions?
2. What is the domain of the function \( h(x) = \frac{1}{x-8} \)?
3. How does the transformation \( g(x) = x - 8 \) affect the graph of \( f(x) \)?
4. Can you express \( h(x) \) in the form \( f(g(x)) \) with a different function \( f(x) \)?
5. How would the function \( h(x) \) change if \( g(x) = x + 8 \)?

**Tip:** When working with composite functions, always substitute the inner function into the outer function to check if they match the given function.

Explore how to express the function h(x) = 1/(x-8) in the form f(g(x)) using function composition. Learn step-by-step with clear examples and understand the concept of composite functions. Suitable for high school students and anyone interested in advanced algebraic concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation