Answer to Question #105496 in Calculus for khushi

Question #105496
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.
1
Expert's answer
2020-03-23T13:55:52-0400

The given function are ,

f(x,y)=2xy and g(x,y)=x2+y2f(x,y)=2xy \ and \ g(x,y)=x^2+y^2

We have to check whether, R2\R^2 is a domain of fg\frac{f}{g} Or not?

Clearly,

f:R2Rf:\R^2\rightarrow \R and g:R2Rg:\R^2\rightarrow \R and g(x,y)=0g(x,y)=0     \iff x=y=0x=y=0

Hence ,Domain of fg\frac{f}{g} is R2(0,0)\R^2 -(0,0) .

Hence the statement is false.


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