Find the Domain z=(y^2)/16-(x^2)/25

Problem

z=(y2)/16−(x2)/25

Solution

1. Identify the type of function. The given expression is a polynomial function in two variables, specifically a quadratic form representing a hyperbolic paraboloid.

2. Check for restrictions such as denominators that could be zero, square roots of negative numbers, or logarithms of non-positive numbers.

3. Observe that the expression consists of subtraction and division by constants (16 and 25, which are defined for all real values of x and y

4. Conclude that there are no values of x or y that make the expression undefined.

Final Answer

Domain={(x,y)∈ℝ2}

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