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The question in the image asks whether the following statement is true or false:

"Let \( f \) and \( g \) each represent functions. The composition function of \( g \) and \( f \) is defined as \( (g \circ f)(x) = f(g(x)) \), where \( x \) is an element in the domain of \( f \), and \( f(x) \) is an element in the domain of \( g \)."

This statement is **False**, and here's why:

The correct definition of the composition of two functions \( g \circ f \) is \( (g \circ f)(x) = g(f(x)) \), not \( f(g(x)) \). Additionally, for the composition \( g(f(x)) \) to be valid:
- \( x \) must belong to the domain of \( f \),
- \( f(x) \) must belong to the domain of \( g \).

Thus, the original statement reverses the order of the composition and is incorrect.

Let me know if you'd like further details or explanations!

Here are 5 questions related to this topic:
1. What are the conditions for the composition of two functions to be defined?
2. How can you determine the domain of a composite function?
3. What is the difference between \( f(g(x)) \) and \( g(f(x)) \)?
4. Can a composite function exist if the range of the inner function does not overlap with the domain of the outer function?
5. How do you evaluate a composite function given specific functions \( f(x) \) and \( g(x) \)?

**Tip**: Always ensure the correct order of function composition—\( (g \circ f)(x) = g(f(x)) \)—when working with composite functions.

Misalkan f dan g masing-masing menyatakan suatu fungsi. Fungsi komposisi dari g dengan f didefinisikan sebagai (g o f)(x) = f(g(x)), dengan x merupakan unsur di domain f dan f(x) merupakan unsur di domain g. Apakah pernyataan ini benar atau salah?

Explore the concepts behind function composition, focusing on how to correctly apply (g o f)(x) = g(f(x)) and the conditions for domain and range. Ideal for students in Grades 9-12 learning advanced algebra.

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