00:01
So in this problem, we're given the mapping for the function f and for the function g.
00:04
What we want to do is to find the domain and the range for the composition of g of f of x.
00:09
Okay.
00:10
So remember, this composition, g of f, means we need to find g of f of x.
00:16
Okay.
00:17
So because we're starting with our f of x function, because remember, we always start with our inside function, that means our domain is going to be all these values for the domain in our f function.
00:27
So now we can actually go ahead and write the domain for our final answer.
00:32
So a set notation, that would mean is to all the values of x, such that it's the same values as your domain for x or for f, which would be 2, 3, 5, 7, and 8.
00:44
So that would be our domain.
00:45
Now, to find the range, we actually have to go ahead and find these values.
00:49
So first, let's start when x is 2.
00:50
So that means we have to find g of f of 2.
00:55
Okay, well, f of 2, that would be 3.
00:57
3.
00:58
So in this case, now we need to find g of 3.
01:01
So we'll go to our mapping for g, and we'll find that g of 3 is equal to 0.
01:06
So 0 will be part of our range.
01:09
The next value in our domain is 3.
01:11
So in this case, we're going to find g of f of 3.
01:16
Okay, well, we go to our mapping for f.
01:19
F of 3 is equal to 5.
01:21
So we'll have g of 5, and then we go to our g mapping, and g of 5 would equal to 1.
01:27
So 1 is in the range.
01:30
Okay.
01:30
Next, let's do 5.
01:32
So we need g of f of 5...