The question in your image appears to involve the floor function, denoted $g(x) = \lfloor x \rfloor$, and is related to the mathematical sets $\mathbb{R}$, $\mathbb{Z}$, and the function $g$.

Let me break it down for clarification:

Definitions:

1. $\mathbb{R}$: The set of all real numbers.
2. $\mathbb{Z}$: The set of all integers.
3. $g(x) = \lfloor x \rfloor$: The floor function, which maps a real number $x$ to the largest integer less than or equal to $x$.

Function Domain and Codomain:

• The floor function $g$ takes an input from $\mathbb{R}$ (real numbers) and outputs a value in $\mathbb{Z}$ (integers). This is usually denoted as: $g: \mathbb{R} \to \mathbb{Z}$

Matching Terms:

Here’s how you might match the given terms:

• $\mathbb{R}$: Domain of $g(x)$.
• $\mathbb{Z}$: Codomain of $g(x)$.
• $g$: The floor function itself.
• $x$: A variable in the domain $\mathbb{R}$.

Would you like further clarification or additional details?

Related Questions:

1. What is the difference between the floor function and the ceiling function?
2. How can we represent $g(x) = \lfloor x \rfloor$ on a graph?
3. Why does $g(x)$ map $\mathbb{R}$ to $\mathbb{Z}$?
4. What happens when $x$ is an integer for $g(x)$?
5. Can the codomain of $g(x)$ be a subset of $\mathbb{Z}$?

Tip:

When analyzing functions, always confirm the domain and codomain explicitly—they define the function's behavior and output set!