1. Let's start by stating the problem: We want to understand how to find the domain of a function. 2. The domain of a function is the set of all possible input values ($x$) for which the function is defined. 3. Important rules to consider when finding domains: - The function cannot have division by zero. - The function cannot have a negative number inside an even root (like square root). - The function must have real values (no complex numbers unless specified). 4. Step-by-step method: - Identify any denominators and set them not equal to zero. - Identify any even roots and set the radicand (expression inside the root) greater than or equal to zero. - Solve these inequalities or equations to find the allowed values of $x$. 5. Example: Find the domain of $f(x) = \frac{1}{\sqrt{x-3}}$. - The denominator $\sqrt{x-3}$ cannot be zero or negative. - So, $x-3 > 0$. - Solve: $x > 3$. - Therefore, the domain is all real numbers greater than 3. 6. Summary: To find the domain, look for restrictions like division by zero or even roots of negative numbers, then solve inequalities to find valid $x$ values. This method works for most functions you will encounter.