00:01
In this video, we're given the fact that they want us to use that h of x is equal to f of x over g of x.
00:06
They also tell me that all the f of x for this ones are 3x minus 1.
00:09
And that because we're given that f of x and essentially the h of x in the different pieces, we're going to find that g of x.
00:15
So before i do anything with the pieces of this problem, i'm going to go ahead and do this in a very general way.
00:19
So if i'm going to give an h of x right here and i know f of x is 3x minus 1, let's kind of work out the math already to figure out what's the easy way to get g of x.
00:28
All right.
00:29
So the first thing i would do is just kind of cross multiply.
00:31
So h of x time g of x would be the first step is equal to 3x minus 1.
00:37
And to get the g of x by itself, i have to divide by h of x.
00:42
All right, essentially, so what's going to happen is, in order to get a g of x, i'm going to take that 3x minus 1 and divide it by h of x.
00:48
Okay.
00:48
So i'm going to do that for each problem that we don't have to work all those little steps out.
00:52
All right.
00:52
So for a for a for a here, our h of x is equal to 3x minus 1 over x plus 7.
01:03
So i'm going to do that division.
01:05
So we're going to do 3x minus 1 over 3x minus 1 over x plus 7.
01:13
All right, don't forget when we divide what fraction of the reciprocal.
01:16
So essentially 3x minus 1 over 1 would stay the same.
01:20
Then i would multiply by x plus 7 over 3x minus 1.
01:24
You multiply the reciprocal.
01:26
And what's going to happen is those 3x minus 1 are going to cross out.
01:29
So our g of x function right here is going to equal to x plus 7.
01:35
And again, me doing all that little work.
01:37
In the beginning to figure out what i really have to do makes it a lot faster.
01:41
The next one, h of x is equal to 3x minus 1 over the square root of x plus 6.
01:48
It's going to be super similar what we just did.
01:51
So i take 3x minus 1 and then divide it by that 3x minus 1 over the square to x plus 6.
01:57
Okay, in the same logic at the multiple of the reciprocal.
01:59
So i'm doing 3x minus 1 over 1 times the square to x plus 6 over 3x minus 1...