How do you find the domain of a function

There are different way but I will give you 2 ways;
1. Learn the definition of the domain. The domain is defined as the set of input values for which the function produces an output value. In other words, the domain is the full set of x-values that can be plugged into a function to produce a y-value.
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2. Learn how to find the domain of a variety of functions. The type of function will determine the best method for finding a domain. Here are the basics that you need to know about each type of function, which will be explained in the next section:
A polynomial function without radicals or variables in the denominator. For this type of function, the domain is all real numbers.
A function with a fraction with a variable in the denominator. To find the domain of this type of function, set the bottom equal to zero and exclude the x value you find when you solve the equation.
A function with a variable inside a radical sign. To find the domain of this type of function, just set the terms inside the radical sign to >0 and solve to find the values that would work for x.
A function using the natural log (ln). Just set the terms in the parentheses to >0 and solve.
A graph. Check out the graph to see which values work for x.
A relation. This will be a list of x and y coordinates. Your domain will simply be a list of x coordinates.