In this article I outline a systematic way of finding the domain of a composite function. A definition that can be used for this purpose follows:

(Vaught, 1995:18)

Where

The explanatory method which follows is to show how to use this definition in different examples.

**Example 1**

Solve .

Solution:

Let

**Example 2.1**

Let and where .

Find

Solution:

**Example 2.2**

Consider the same constraints as in Example 2.1, but with

Solution:

**References**

Vaught, RL. 1995. Set theory: An introduction. 2nd edition. Boston: Birkhäuser.

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