Question

Multivariable calculus help needed here :D
Find the codomain of function f(x,y) = ( Log(xy), 1/(x^2 + y^2) ), where 0 < y < x

Answer 1

\[f(x,y)=(\ln x y, \frac{ 1 }{ x^2 + y^2 })\]

Answer 2

minus (0,0)

Answer 3

I know that the answer is positive part under the graph of function \[e^{-x}\], but I don't know how to obtain it.

Answer 4

just look where the function will be defined

Answer 5

That's the domain, I need the codomain, i.e. the image of this function.

Answer 6

Log[xy] => this will range all over R
1/(x^2+y^2) => this will range all over Positive R