Find the range of $f ( x , y ) = \frac { x } { x ^ { 2 } - y ^ { 2 } }$
A) $R$
B) $[ 0 , \infty )$
C) $( - \infty , 0 )$
D) $( - 1,1 )$

Question

Quizplus · Accepted Answer

The function $f(x, y) = \frac{x}{x^2 - y^2}$ can take any real value except when the denominator is zero, which happens when $x^2 = y^2$. This means the function can approach any real number by choosing appropriate values of $x$ and $y$, thus its range is all real numbers, $R$.

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

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