Domain Of A Function In Set Builder Notation

If the domain of a function is all real numbers i e.

Domain of a function in set builder notation. Set builder notation is very useful for defining domains. In its simplest form the domain is the set of all the values that go into a function. All the real numbers from 0 onwards because there s no square root of a negative number x r x 0 1 x 2 1 all the real numbers except 1 and 1 because 1 x 2 1 is undefined at x 1 or x 1 x r x 1 x 1.

All the real numbers except 0 because 1 x is undefined at x 0 x r x 0 x. The domains and ranges used in the discrete function examples were simplified versions of set notation. For example instead of making a list of all counting numbers smaller than 1000 it is more convenient to write x x is a counting number less than 100 it is also very useful to use a set builder notation to describe the domain of a function.

We can also use inequalities or other statements that might define sets of values or data to describe the behavior of the variable in set builder notation. For example latex left x 10 le x 30 right latex describes the behavior of latex x latex in set builder notation. In the previous examples we used inequalities and lists to describe the domain of functions.

Thanks for contributing an answer to mathematics stack exchange. Asking for help clarification or responding to other answers. When using set notation we use inequality symbols to describe the domain and range as a set of values.

For a function f x 2 x 1 f x 2 x 1. Please be sure to answer the question provide details and share your research. There are no restrictions on x you can simply state the domain as all real numbers or use the symbol to represent all real numbers.

If f x 2 x 5 the domain of f is x x is not equal to 5. The domain of 1 x. The domain is therefore r except x 3.