Question

Consider the function below.

f(x, y) = √1 + x - y2
(a) Find and sketch the domain of the function. (Do this on paper. Your instructor may ask you to turn in this work.)
x ---Select--- > = ≥

Answer 1

The domain of the function f(x, y) = √1 + x - y² is x ≥ y² - 1. The sketch of this domain is represented by a parabola opening to the right, with its vertex at (-1, 0), and includes everything to the right of this parabola.

Step-by-step explanation:

This is a Mathematical concept related to functions. The domain of a function is the set of all possible input values (x-values) which will produce a valid output. In this question, you are asked to find the domain of the function f(x, y) = √1 + x - y².

For the function to have a real output, the quantity under the square root must be non-negative. So, we set 1 + x - y² ≥ 0. Now, we solve for x in terms of y which gives x ≥ y² - 1.

This represents the domain of the function which is: x is greater than or equal to y² - 1.

To sketch this domain, you would draw a graph with a parabola opening to the right, its vertex at (x, y) = (-1, 0). Everything to the right of this parabola including the parabola itself is part of the domain.

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