At what points is the given function continuous?
-$$f ( x , y , z ) = \frac { 1 } { | x - 3 | + | y - 4 | + | z - 5 | }$$
A) All $( x , y , z ) \neq ( 3,4,5 )$
B) All $( x , y , z )$
C) All $( x , y , z ) \neq ( 0,0,0 )$
D) All $( x , y , z ) \neq \pm ( 3,4,5 )$

Question

Quizplus · Accepted Answer

The function is continuous everywhere except at the point where the denominator becomes zero, which happens at $ ( x , y , z ) = ( 3,4,5 )$. At this point, the function is undefined, making it discontinuous only there.

At What Points Is the Given Function Continuous? - f(x,y,z)=1∣x−3∣+∣y−4∣+∣z−5∣f ( x , y , z ) = \frac { 1 } { | x - 3 | + | y - 4 | + | z - 5 | }f(x,y,z)=∣x−3∣+∣y−4∣+∣z−5∣1​

At What Points Is the Given Function Continuous?
- $f ( x , y , z ) = \frac { 1 } { | x - 3 | + | y - 4 | + | z - 5 | }$