At what points is the given function continuous?
-$$f ( x , y ) = \frac { x y } { x + y }$$
A) All $( x , y )$ such that $x \neq y$
B) All $( x , y ) \neq ( 0,0 )$
C) All $( x , y )$
D) All $( x , y )$ such that $x \neq - y$

Question

Quizplus · Accepted Answer

The function $f(x, y) = \frac{xy}{x+y}$ is undefined when the denominator is zero, which occurs when $x + y = 0$ or equivalently when $x = -y$. For all other points, the function is defined and continuous.

At What Points Is the Given Function Continuous? - f(x,y)=xyx+yf ( x , y ) = \frac { x y } { x + y }f(x,y)=x+yxy​

At What Points Is the Given Function Continuous?
- $f ( x , y ) = \frac { x y } { x + y }$