Find the range of the function $f ( x , y ) = \ln \left( x - y ^ { 2 } \right)$ .
A) $( 0 , \infty )$

B) $[ 0 , \infty )$
C) $( - \infty , \infty )$
D) $( - \infty , 0 )$
E) $( 1 , \infty )$
F) $[ 1 , \infty )$

G) $( \sqrt { 2 } , \infty )$

H) $[ \sqrt { 2 } , \infty )$

Question

Find the range of the function $f ( x , y ) = \ln \left( x - y ^ { 2 } \right)$ .
A) $( 0 , \infty )$

B) $[ 0 , \infty )$ 
C) $( - \infty , \infty )$
D) $( - \infty , 0 )$ 
E) $( 1 , \infty )$ 
F) $[ 1 , \infty )$ 
 
G) $( \sqrt { 2 } , \infty )$

H) $[ \sqrt { 2 } , \infty )$

Quizplus · Accepted Answer

The argument of the logarithm function, $x - y^2$, must be positive for the function to be real-valued, meaning $x - y^2 > 0$. This implies that the function can take on any value from negative infinity to positive infinity as the logarithm can approach negative infinity as its argument approaches zero from the right and positive infinity as its argument increases without bound.

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

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