Final answer:
To determine where the function f(x, y) is continuous, we need to find where its denominator is non-zero. This involves solving the inequality involving x and y to avoid division by zero, ensuring the function is defined and has no discontinuities.
Step-by-step explanation:
The question asks to determine the set of points at which the given function f(x, y) = 1/(x² y² 5 - x² - y²) is continuous. To find out where the function is continuous, we need to identify the points at which the function is defined, which means finding where the denominator is not zero. A function is continuous at a point if it is defined there and if the limit of the function as it approaches the point is equal to the function's value at that point.
We need to ensure that the denominator x² y² 5 - x² - y² is not equal to zero to avoid division by zero, which is undefined. Therefore, we solve the inequality x² y² 5 - x² - y² ≠ 0 to find out the values of x and y for which the function is continuous. The continuity of a function is closely related to its graph since a continuous function has no breaks, jumps, or holes in its graph.