Answer: To find the domain of a function, you need to identify all the possible input values (x) for which the function produces a valid output (y). In other words, you need to find the set of all values of x for which the function is defined and produces real outputs.
Step-by-step explanation: Here are the general steps to find the domain of a function:
Look for any values of x that could lead to undefined results. For example, if the function involves a square root, the value inside the square root cannot be negative, so you need to ensure that the expression inside the square root is non-negative.
Look for any values of x that could lead to division by zero. For example, if the function involves a fraction, the denominator cannot be zero, so you need to ensure that the denominator is not equal to zero.
Look for any other restrictions on the input values based on the definition of the function. For example, some functions may require that x be a certain type of number, such as an integer or a positive real number.
Write the domain of the function as a set of possible input values. For example, you might write the domain as an interval of real numbers or a set of discrete values.
It is important to note that some functions may have restricted domains due to the nature of the function, while other functions may have unrestricted domains that encompass all real numbers.