# Domain of a Function of Two Variables

Domain of a Function of Two Variables

The domain of a function is the set of ordered pairs for which the function is well defined. If there is no value of corresponding to the point , then it is not in the domain of the function.

z=f(x,y)

(x,y)

f(x,y)

z

(x,y)

In this Demonstration, the function is plotted as the blue surface above the artificially constructed domain .

0.1x-x+50sin(x)-4-3y

3

2

2

y

2

(x,y)|30<x+y<100,x+(9-y)<110,(9-x)+y<85

2

2

2

2

2

2

More realistic domains include situations with a physical constraint like a wall or economic constraints like a limit imposed by an ad hoc law. In mathematics, restricted domains can arise when function becomes complex-valued or has a natural boundary.