Domain of a Function of Two Variables

x

5

y

5

(x, y) ∈ the domain of f

The domain of a function

z=f(x,y)

is the set of ordered pairs

(x,y)

for which the function

f(x,y)

is well defined. If there is no value of

z

corresponding to the point

(x,y)

, then it is not in the domain of the function.

In this Demonstration, the function

0.1

3

x

-

2

x

+50

2

sin

(x)-4

2

y

-3y

is plotted as the blue surface above the artificially constructed domain

(x,y)30<

2

x

+

2

y

<100,

2

x

+

2

(9-y)

<110,

2

(9-x)

+

2

y

<85

.

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.