ASK A QUESTION At what points (x, y, z) in space is the function f(x,y,z)=(x^2+y^2-1)^(1/2) continuous?

Question

what's the procedure...??

Answer 1

There is no z in the expression for the function.  Is there a typo in the problem statement?  Anyway, I will answer the problem as currently stated.

 

f = √(x² + y² - 1)

 

The argument of the square root must not be negative, so you have the restriction that

 

x² + y² ≥ 1

 

This means you must not be inside a circle of radius 1, but you can be on the circle or outside the circle.