# Thread: g(x,y)=f(x,y) for all (x,y)

1. ## g(x,y)=f(x,y) for all (x,y)

f(x,y)=(x)/ (1-y2), y does not equal 1 or -1

Is it possible to define a new function g(x,y) that is defined and continuous for all (x,y) in R2, and such that g(x,y)=f(x,y) for all (x,y) in the domain of f? If so, find such a function. If not, explain why.

I really don't know where to begin...

2. Originally Posted by genlovesmusic09
f(x,y)=(x)/ (1-y2), y does not equal 1 or -1

Is it possible to define a new function g(x,y) that is defined and continuous for all (x,y) in R2, and such that g(x,y)=f(x,y) for all (x,y) in the domain of f? If so, find such a function. If not, explain why.

I really don't know where to begin...

because that function is defined and continuous...

3. Originally Posted by genlovesmusic09
Indeed, but $\displaystyle g(x,y)\neq f(x,y)$...for example, $\displaystyle g(1,2)=\frac{1}{5}\neq -\frac{1}{3}=f(1,2)$
The problem has no solution since $\displaystyle f$ cannot be redefined (which in fact is what you want) in $\displaystyle \pm 1$ as $\displaystyle \lim_{(x,y)\to (x_0,\pm 1)}f(x,y)$ doesn't exist.