Question

Determine the domain and range of f(x, y) = √x √y.

a) [0, [infinity]), [0, [infinity])
b) (-[infinity], [infinity]), [0, [infinity])
c) [0, [infinity]), (-[infinity], [infinity])
d) (-[infinity], [infinity]), (-[infinity], [infinity])

Answer 1

The domain of the function is [0, +∞) for both x and y, and the range of the function is also [0, +∞).

Step-by-step explanation:

The domain of a function represents all possible values that the independent variable can take on, while the range represents all possible values that the dependent variable can take on.

In the given function, f(x, y) = √x √y, the square root function is defined for non-negative values.

Therefore, the domain of the function is [0, +∞) for both x and y. For example, if x = 4 and y = 9, the function would be f(4, 9) = 2 * 3 = 6.

Hence, the answer is option a) [0, +∞), [0, +∞).