00:01
We solve the problem, find and sketch the domain of the function fxyc equals square 1 minus x squared minus y square minus x squared minus y square minus z square.
00:13
First, what is the domain? the domain simply is the set of all possible values or maybe you can say input that make valid output.
00:50
Okay, so in this function, f, the input is x, y, z, right? so in this case, input, or the values that we are going to put into the function, is x, y, z.
01:09
And the output will be the value of this, which is square root 1 minus x, square, minus y, square, minus c squared.
01:20
So the question is, what will make square root 1 minus x square minus y square minus c squared? valid.
01:33
So the answer is you need to know that under the square root, inside or under the square root here must be bigger or equal than zero.
01:45
It cannot be negative.
01:48
Okay.
01:49
That means what we have here is under the square root is 1 minus x square, minus y square minus c square must be bigger all equal than zero and then you just move it around make it nice so we get x squared plus y square plus c square less than all equal than one right this this way you just move this to the other side and then flip flip the inequality you will get this so you want the domain...