# Math 22 Functions of Several Variables

Jump to navigation
Jump to search

## Definition of a Function of Two Variables

Let be a set of ordered pairs of real numbers. If to each ordered pair in there corresponds a unique real number , then is a function of and . The set is the domain of , and the corresponding set of values for is the range of . Functions of three, four, or more variables are defined similarly.

**Exercises 1** Given . Evaluate:

**1)**

Solution: |
---|

So, |

**2)**

Solution: |
---|

So, |

**3)**

Solution: |
---|

So, |

**4)**

Solution: |
---|

So, |

## The Domain and Range of a Function of Two Variables

**Example:** Find the domain of

Notice that : The radicand should be non-negative. So, , hence the domain is .

Notice: is the circle center at , radius 3.

Since the point satisfies the inequality . Hence the range is

**This page were made by Tri Phan**