1. The problem asks for the domain of the function $A = \pi x^2$, where $A$ is the area of a circle and $x$ is the radius. 2. The formula for the area of a circle is $A = \pi r^2$, where $r$ is the radius. Since radius represents a length, it must be non-negative. 3. Therefore, the domain of $A(x) = \pi x^2$ is all real numbers $x$ such that $x \geq 0$, which is the set of non-negative real numbers. 4. Among the options given: - a) $\mathbb{R}$ (all real numbers) includes negative values, which are not valid for radius. - b) $\mathbb{R} - \{0\}$ excludes zero but radius can be zero. - c) $\mathbb{Z}^+$ (positive integers) is too restrictive since radius can be any positive real number. - d) $\mathbb{R}^+$ (positive real numbers) excludes zero but radius can be zero. 5. Since radius can be zero or any positive real number, the domain is $\{x \in \mathbb{R} : x \geq 0\}$, which is the set of non-negative real numbers. This is closest to option d) if we consider $\mathbb{R}^+$ to include zero, but usually $\mathbb{R}^+$ means strictly positive. 6. The best choice is d) $\mathbb{R}^+$ assuming it includes zero or the problem intends positive real numbers including zero. Final answer: d) $\mathbb{R}^+$