Final answer:
To find and sketch the domain of the given function, we need to ensure that the square root term is non-negative and exclude the values of x where the denominator is zero.
Step-by-step explanation:
To find and sketch the domain of the function f(x, y) = √(y-x²)/(16-x²), we need to determine the set of values for x and y that make the function well-defined.
First, we note that the function has a square root term. To ensure that the term inside the square root is non-negative, we need (y-x²)/(16-x²) ≥ 0. This condition implies that either both the numerator and denominator are positive or both are negative.
Next, we note that the denominator cannot be zero. Therefore, we have to exclude the values of x where 16-x² = 0. Solving this equation, we find x = -4 and x = 4.
Therefore, the domain of the function f(x, y) = √(y-x²)/(16-x²) is all values of x such that x ≠ -4 and x ≠ 4.