At what points is the given function continuous?
-$$f ( x , y ) = \frac { x - y } { 2 x ^ { 2 } + x - 6 }$$
A) All $( x , y )$ such that $x \neq 0$
B) All $( x , y )$
C) All $( x , y )$ satisfying $x - y \neq 0$
D) All $( x , y )$ such that $x \neq \frac { 3 } { 2 }$ and $x \neq - 2$

Question

Quizplus · Accepted Answer

The continuity of the function depends on the denominator $2x^2 + x - 6$ since the numerator $x - y$ does not impose any restrictions on $x$ or $y$ for continuity. Factoring the denominator gives $(2x - 3)(x + 2)$, which is zero when $x = \frac{3}{2}$ or $x = -2$. Therefore, the function is continuous for all $(x, y)$ except when $x = \frac{3}{2}$ or $x = -2$.

At What Points Is the Given Function Continuous? - f(x,y)=x−y2x2+x−6f ( x , y ) = \frac { x - y } { 2 x ^ { 2 } + x - 6 }f(x,y)=2x2+x−6x−y​

At What Points Is the Given Function Continuous?
- $f ( x , y ) = \frac { x - y } { 2 x ^ { 2 } + x - 6 }$