The domain of the function $f ( x , y ) = \ln \left( 2 x ^ { 2 } - y ^ { 2 } \right)$ is

A) $\{ ( x , y ) : ( x , y ) \neq ( 0,0 ) \}$
B) $\{ ( x , y ) : 2 x \neq y \}$
C) $\left\{ ( x , y ) : y ^ { 2 }

Question

The domain of the function $f ( x , y ) = \ln \left( 2 x ^ { 2 } - y ^ { 2 } \right)$ is

A) $\{ ( x , y ) : ( x , y ) \neq ( 0,0 ) \}$
B) $\{ ( x , y ) : 2 x \neq y \}$
C) $\left\{ ( x , y ) : y ^ { 2 } < 2 x ^ { 2 } \right\}$
D) $\{ ( x , y ) : y \neq \sqrt { 2 } x \}$
E) $\{ ( x , y ) : - \infty < x < \infty , - \infty < y < \infty \}$

Quizplus · Accepted Answer

The argument of the logarithm function, $2x^2 - y^2$, must be greater than zero for the function to be defined. Therefore, the domain is $\{ ( x , y ) : y^2 < 2x^2 \}$, which matches choice C.

The Domain of the Function f(x,y)=ln⁡(2x2−y2)f ( x , y ) = \ln \left( 2 x ^ { 2 } - y ^ { 2 } \right)f(x,y)=ln(2x2−y2)

The Domain of the Function $f ( x , y ) = \ln \left( 2 x ^ { 2 } - y ^ { 2 } \right)$