Give the domain and range of the multi-variable function.
\(f(x; y) = x^2 + y^2 + 2\)
Solution
\(f(x; y) = x^2 + y^2 + 2\)
\(z = f(x,y)\)
For all possible pairs of (x,y), domain of z is \(R^2\).
The range is the set of all possible output values. The square ensures that all output is >= 0. Since the x and y terms are squared, then add with 2, the largest output value comes at x = 0, y = 0: f(0; 0) = 2.
Thus the range R is the interval [2, \(\infty\)).
Most valuable elements you took away from this course?
I love doing derivatives and integrations, this course gives me the chance to refresh my calculus skill. Got the opportunity to work on vectors, matrix operations, probability, linear transformation problems by hand as well as using predefined functions. This course designed to get good fundamentals of linear algebra, probability, calculus, and Regression concepts.