Question

Let g(x, y) = cos(x + 2y). (a) Evaluate g(2, -1). (b) Find the domain of g. (c) Find the range of g. 1. Find and sketch the domain of the function f(x, y) =sqrt(y-x^2)/(1-x^2) 2. Draw a contour map of the function f(x, y) = ye^-x showing several level curves. 3. Sketch both a contour map and a graph of the function f(x, y) = x^2 + 9y^2.

Answer 1

Not going to do (1), (2), (3) since they are implicit from (a) and (b) and require graphs (which aren't supported on brainly).

We have $g(x,y)=\cos(x+2y)$, that means, if plug in $x=2,y=-1$ we get $g(2,-1)=\cos(2+2(-1))=\cos(0)=\boxed{1}$.

Doman of cosine is $x\in[0,1]$.

Hope this helps.