Determine the largest possible domain of a function
Determine the largest possible domain of a function
Example (1) : Determine the largest possible domain of f (x, y) = ( 2x + 3 3y.
Solution: Any real value of y can make 3 3y meaningful, and so the domain for 3 3y is the
whole y-axis. Only non negative real value of x can make 2x meaningful, and so the domain for
2x is the half line [0, ). Combining these facts, we conclude that the domain of the function
f (x, y) = ( 2x + 3 3y is the half plane where x 0, or in set notation: {(x, y) : 0 x <
and - < y < }.
xy Example (2) : Determine the largest possible domain of f (x, y) = x2 - y2 .
Solution: To avoid zero denominators, we must have x2 -y2 = 0. Since x2 -y2 = (x-y)(x+y),
the domain of this function is the whole xy-plane with the two straight lines y = x and y = -x
taken away.
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