Example 7

Find a set where the function

is continuous.

• x² is continuous for all x.
• x²y is continuous for all (x, y).
• x + y is continuous for all (x, y).
• (x + y) + z is continuous for all (x, y, z).
• is continuous for x + y + z ≠ 0.

Answer h(x, y, z) is continuous on the set of all (x, y, z) such that x + y + z ≠ 0.