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.