00:01
For this problem, we are asked to describe the domain and range of the function f of x, y, z, equals the square root of 16 minus r squared, s squared, t squared.
00:09
So we can start with the domain here.
00:12
We can tell, since we have this square root, we know that the square root has to have an argument, or the thing inside of the square root, has to be greater than zero.
00:20
So we have then that 16 must be greater than or equal to r squared times s squared times t squared.
00:29
So we can segment this off in various ways, if we wanted to, putting one variable in terms of the other, or in terms of the other two, but we won't be able to get any sort of neat, closed expression doing it that way.
00:43
So the best way to express the domain here is just going to be that it's the entirety of the three -dimensional real numbers, such that r squared times s squared times t squared is less than or equal to 16...