00:01
Okay, so in this question we have g of x is equal to the floor of x and we want to find the pre -image of the set of zero so let's think about how we can do this if we think about our number line have zero one and minus one so what numbers of x gives us zero? well because the floor functions give us the integer which is strictly below it then any number that occurs between zero and one is going to get mapped all the way back to zero.
00:41
Importantly we exclude one.
00:43
So then the pre -image of this set is just zero less than equal to x less than one.
00:50
Oh sorry i should write that a couple of the pre -image of zero.
00:55
It's just an interval from zero to one.
01:00
Now we have the pre -image of the set minus 1, 0 and 1.
01:06
So we know if we just expand this a bit more and minus 2.
01:12
So we know that from this case, we're just going to take the integer first up and we're going to map it down.
01:17
So to get 1, it's going to be from 2 gets mapped down...