Identifying the domain and range of a function is very important when solving equations. They help us know what inputs we can use and what outputs we can expect. Let’s break it down into simpler parts:

1. What is Domain?
The domain of a function is all the possible input values, often shown as $x$. For example, look at the function $f(x) = \sqrt{x}$. The domain here is $x \geq 0$. This means you can only use numbers that are zero or positive. You can't take the square root of a negative number. Knowing the domain is useful when solving problems because it keeps you from using numbers that don’t work.

2. What is Range?
The range is all the possible output values, which we usually call $y$. For our earlier example, since $f(x) = \sqrt{x}$ gives results starting from 0 and going up, we say the range is $y \geq 0$. Understanding the range helps us see how the function behaves, especially when we’re looking for outputs based on certain inputs.

3. Why is This Important for Solving Problems?
When we solve equations, especially with things like inequalities or where two functions meet, knowing the domain and range helps us focus on the right values. For example, if we need to solve $f(x) = 3$ and we know the domain is $x \geq 0$, we won't waste time checking negative numbers, since they won’t give us a solution.

4. Example with Graphs:
When we graph $f(x) = 1/x$, it’s really important to know that the domain does not allow $x = 0$. If we tried to divide by zero, we would get an error. The graph will show that there is a vertical line, called an asymptote, at $x = 0$. For the range, all real numbers are included except for $y = 0$. This shows us how the function works.

In summary, knowing the domain and range is like having a map that guides us when solving equations. It helps us find correct solutions and understand how the function behaves.