Answer to Question #105496 in Calculus for khushi

Question

State whether the following statements are true or false. Give reasons for your answers 3) The domain of the f/g where f(x, y) =2xy and g(x, y) =x^2+y^2 is R^2.

Answer 1

The given function are ,

$f(x,y)=2xy \ and \ g(x,y)=x^2+y^2$

We have to check whether, $\R^2$ is a domain of $\frac{f}{g}$ Or not?

Clearly,

$f:\R^2\rightarrow \R$ and $g:\R^2\rightarrow \R$ and $g(x,y)=0$ $\iff$ $x=y=0$

Hence ,Domain of $\frac{f}{g}$ is $\R^2 -(0,0)$ .

Hence the statement is false.