Domain And Range Set Notation Examples

Set builder notation for domain and range set builder notation is very useful for defining the domain and range of a function.

Domain and range set notation examples. As a more extreme example a function s inputs and outputs can be completely different categories for example names of weekdays as inputs and numbers as outputs as on an. For example the union of the sets latex left 2 3 5 right latex and latex left 4 6 right latex is the set latex left 2 3 4 5 6 right latex. The domains and ranges used in the discrete function examples were simplified versions of set notation.

Calculate the domain and the range of the function f x 2 x. The domain of f x x 2 in set notation is. For our example we would use set notation in the following way.

Range is a little trickier to nd than domain. Before we look at some examples lets talk for a little bit about range. For a function f x 2 x 1 f x 2 x 1.

Set the denominator equal to zero and solve for x. For example the function latex f left x right frac 1 sqrt x latex has the set of all positive real numbers as its domain but the set of all negative real numbers as its range. Find the domain and range of the following function.

F x 2 x 1 solution. Everything else is ok. As a more extreme example a function s inputs and outputs can be completely different categories for example names of weekdays as inputs and numbers as outputs as on an attendance chart in such cases the domain and range have no elements in common.

For example the function f x 1 x f x 1 x has the set of all positive real numbers as its domain but the set of all negative real numbers as its range. In its simplest form the domain is the set of all the values that go into a function. Set the denominator to zero.