1. The problem is to find the domain of definition of a function, which means determining all possible input values $x$ for which the function is defined. 2. The domain depends on the type of function and any restrictions such as division by zero, square roots of negative numbers, or logarithms of non-positive numbers. 3. Important rules: - For fractions, the denominator cannot be zero. - For square roots (or even roots), the radicand must be $\geq 0$. - For logarithms, the argument must be $> 0$. 4. To find the domain: - Identify any denominators and set them $\neq 0$. - Identify any even roots and set the radicand $\geq 0$. - Identify any logarithms and set the argument $> 0$. 5. Solve these inequalities or equations to find the intervals of $x$ that satisfy all conditions. 6. The domain is the intersection of all these intervals. Example: For $f(x) = \frac{1}{\sqrt{x-2}}$, - Denominator $\sqrt{x-2} \neq 0$ means $x-2 > 0$ (since square root must be positive and denominator nonzero). - So domain is $x > 2$. This method applies generally to find the domain of any function.