DATA 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS

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Give the domain and range of the multivariable function.

8. \(f(x, y) = x + 2y\)

domain: \(\mathbb{R}^2\)

range: \(\mathbb{R}\)

14. \(f(x, y) = \frac{1}{\sqrt{x^2 + y^2 - 9}}\)

domain: \(\{(x, y)|x^2 + y^2 > 9\}\) , i.e., the domain lies outside of a circle centered at the origin with radius 3.

range: \(z > 0\)