Question

Find the domain and range of the function f, defined by f(x,y) = 2xy/( x²+y ²) . Also find two level curves of this function. Give a rough sketch of them.

Answer 1

Domain: $\{(x,y)\isin R^2:x^2+y^2>0\}$

Range: $\{z\isin R:-1\le z\le 1\}$