1. The problem is to understand the concepts of domain and range of a function. 2. The domain of a function is the set of all possible input values (usually $x$) for which the function is defined. 3. The range of a function is the set of all possible output values (usually $y$) that the function can produce. 4. To find the domain, identify values of $x$ that do not cause any mathematical issues such as division by zero or taking the square root of a negative number. 5. To find the range, analyze the function's behavior or solve for $x$ in terms of $y$ and determine possible $y$ values. 6. For example, for the function $f(x) = \sqrt{x}$, the domain is $x \geq 0$ because square roots of negative numbers are not real. 7. The range of $f(x) = \sqrt{x}$ is $y \geq 0$ because square roots produce non-negative outputs. This explanation applies generally to any function to determine its domain and range.