# Math Help - Multivariate function Image

1. ## Multivariate function Image

if F: reals^2 --à reals ^2 is defined by F(u,v):=(u/(1+v),uv/(1+v) =: (x(u,v),y(u,v))
And W is the rectangle {(u,v) s.t. 0< or = u < or = 2, 0 < or equal v < or equal 1} in u-v space
could someone describe the image F(W) in x-y space by first showing F^(-1)[(x,y)]=(x+y,y/x)=: (u(x,y),v(x,y))

2. Originally Posted by maximus101
if F: reals^2 --à reals ^2 is defined by F(u,v):=(u/(1+v),uv/(1+v) =: (x(u,v),y(u,v))
And W is the rectangle {(u,v) s.t. 0< or = u < or = 2, 0 < or equal v < or equal 1} in u-v space
could someone describe the image F(W) in x-y space by first showing F^(-1)[(x,y)]=(x+y,y/x)=: (u(x,y),v(x,y))
First Hello and welcome to the forum. You have been posting alot of questions. I would recommend you learn LaTex. See here http://www.mathhelpforum.com/math-help/f47/

Note you can also click on the math symbols to see the code that generated them.

Note that you have the system of equations.

$\displaystyle x=\frac{u}{1+v}$ and $\displaystyle y=\frac{uv}{1+v}$

This implies that $\displaystyle xv=\frac{uv}{1+v}=y \implies v=\frac{y}{x}$

Now using this we get

$\displaystyle x=\frac{u}{1+v} \iff u=(1+v)x=\left( 1+\frac{y}{x}\right)x=x+y$

Can you finish from here?