Find the domain of $f ( x , y ) = \frac { x } { x ^ { 2 } - y ^ { 2 } }$
A) $\operatorname { Dom } ( f ) = \left\{ ( x , y ) \in R ^ { 2 } : x \neq y \right\}$
B) $\operatorname { Dom } ( f ) = \left\{ ( x , y ) \in R ^ { 2 } : x \neq - y \right\}$
C) $\operatorname { Dom } ( f ) = \left\{ ( x , y ) \in R ^ { 2 } : | x | \neq | y | \right\}$
D) $\operatorname { Dom } ( f ) = R ^ { 2 }$

Question

Quizplus · Accepted Answer

The domain of $f(x, y)$ excludes points where the denominator $x^2 - y^2$ equals zero. This occurs when $x^2 = y^2$, or equivalently, $|x| = |y|$. Thus, the domain includes all $(x, y)$ pairs except those where the absolute values of $x$ and $y$ are equal.

Find the Domain Of f(x,y)=xx2−y2f ( x , y ) = \frac { x } { x ^ { 2 } - y ^ { 2 } }f(x,y)=x2−y2x​

Find the Domain Of $f ( x , y ) = \frac { x } { x ^ { 2 } - y ^ { 2 } }$