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We are asked to express the function \( h(x) = \frac{1}{x - 2} \) in the form \( f \circ g \), where \( g(x) = x - 2 \), and we need to find the function \( f(x) \).

To solve this, we follow these steps:

1. We are given that \( g(x) = x - 2 \), and we know that \( h(x) = f(g(x)) \).
2. To express \( h(x) \) in terms of \( f(x) \), substitute \( g(x) \) into \( h(x) \):
   \[
   h(x) = \frac{1}{x - 2} = f(g(x)) = f(x - 2).
   \]
3. This implies that \( f(x - 2) = \frac{1}{x - 2} \).
4. Therefore, the function \( f(x) \) must be:
   \[
   f(x) = \frac{1}{x}.
   \]

Thus, the function \( f(x) \) is \( f(x) = \frac{1}{x} \).

Let me know if you would like further explanation or have any other questions!

Here are some related questions:
1. What is the composition of functions \( f \circ g \)?
2. How do you find the inverse of a composite function?
3. How does the transformation \( g(x) = x - 2 \) affect the graph of a function?
4. How do you verify the composition of two functions?
5. Can you express \( h(x) = \frac{1}{x+3} \) in the form \( f \circ g \)?

**Tip**: When decomposing functions into compositions, it's helpful to identify the inner and outer functions based on transformations applied to the variable.

Express the function h(x) = 1/(x - 2) in the form f ∘ g. If g(x) = (x - 2), find the function f(x).

Learn how to express the function h(x) = 1/(x - 2) in the form of composition using f ∘ g, where g(x) = x - 2. This problem explores algebraic concepts of function composition and inverse functions, suitable for high school students in Grades 9-12.

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