At what points is the given function continuous?
-f(x, y, z) = ln(x + y + z - 6)
A) All $( x , y , z )$ such that $x + y + z \geq 6$
B) All $( x , y , z )$ such that $x + y + z 6$
C) All $( x , y , z )$ in the first octant
D) $\operatorname { All } ( x , y , z )$

Question

At what points is the given function continuous?
-f(x, y, z) = ln(x + y + z - 6) 
A) All $( x , y , z )$ such that $x + y + z \geq 6$
B) All $( x , y , z )$ such that $x + y + z > 6$
C) All $( x , y , z )$ in the first octant
D) $\operatorname { All } ( x , y , z )$

Quizplus · Accepted Answer

The function ln(x + y + z - 6) is not defined when x + y + z - 6 ≤ 0.
So, the function is not continuous at the plane x + y + z = 6. 
Therefore, all points on this plane should be excluded from the domain of the function. 
Hence, the function is continuous for all points in the region x + y + z > 6.

At What Points Is the Given Function Continuous? -F(x, Y (x,y,z)( x , y , z )(x,y,z)

At What Points Is the Given Function Continuous?
-F(x, Y $( x , y , z )$