00:01
For this problem, we are asked to assuming that the function remains real, compute the domain and range of the given function, and plot the level curves.
00:09
So for one thing, we can see that we need to have, or for determining the domain, we need to have 1 minus 2x minus 3y, be strictly or be greater than or equal to 0, which then means that we need to have 1 be greater than or equal to 2x plus 3y.
00:28
And so that's really the best way that we can actually try describing this.
00:33
So that would be our domain.
00:38
And then, for our range, can see that a typical square root function would be able to take on any real value greater than zero.
00:49
Pardon me.
00:50
It would be typically you'd be able to take on any value greater than or equal to zero.
00:57
In this case, we could easily say, for instance, at y equals zero and x equals one half, we would have root 1 minus 1, so we'd get a value of 0.
01:06
And then, if we wanted to get an arbitrarily large value, we could make x, for instance, arbitrarily negative while leaving y at 0, and we'd be able to go off towards infinity.
01:17
So the range is going to be 0, less than or equal to f of x, y, less than infinity.
01:24
And then for plotting the level curves, what we'd do, so we'd have c equals root 1 minus 2x minus 3y.
01:31
So that means c squared equals 1 minus 2x minus 3y.
01:39
So we can then write that 3y is going to be equal to 1 minus 2x minus c squared...