00:01
So in this problem, you're told that f of x is equal x to the fourth, and g of x is equal to x raised to the one fourth power, which, keep in mind, is the same thing as the fourth of x.
00:10
So the first thing we want to do is to find the composite function, f of g of x.
00:15
So i typically like reading it is f of g of x.
00:19
So if we need to find us, we always start with our inside function, which in this case is our g of x function.
00:24
So that means we're going to have f of g of x, which is x to the one fourth power.
00:29
So now we can find f of x to the one -fourth power by substituting x to the one -fourth in place of x in our f -function.
00:37
So that means we have x to the one -fourth power, all raised to the fourth.
00:41
Well, according to our rules for exponents, to simplify, we just need to multiply these.
00:47
Well, one -fourth times four is equal to one, so that means we'll just be left with x.
00:51
So that would be our composite function.
00:53
Well, we also have to find the domain.
00:55
Now you have to be careful.
00:56
You want to look at your final answer, which is x.
00:58
That doesn't have any domain issues.
01:00
But you also have to look at your input.
01:02
Remember, that was the fourth root of x.
01:04
Well, because it's the fourth root, that can't be a negative value.
01:07
So that tells us the domain, in this case, will be all values of x that are greater than are equal to zero.
01:14
So that would be the domain.
01:16
Okay...