00:05
In this problem, we're going to deal with function operations.
00:12
If we are told that h of x is equal to f minus g of x, and we know that f of x is 5x plus 2, then we can find what g of x is equal to given different h of x functions.
00:30
This is a substitution problem.
00:33
So let's say part a that we're told h of x, is equal to negative x squared plus 5x plus 3.
00:47
And we want to figure out what g of x is equal to.
00:55
I'm going to substitute what i know h of x is into this given equation, and i'm going to substitute what i know f of x is again into this equation.
01:15
And in doing so, i'll be left with the function g of x.
01:23
So let's try it out.
01:26
I know h of x is negative x squared plus 5x plus 3.
01:34
And that's equal to f, which is 5x plus 2, minus g of x.
01:47
So i'm going to use algebra and solve for g of x.
01:51
Subtract the 5x.
01:55
So i'm going from the right to the left, subtract the two.
02:00
That cancels this side out.
02:04
And that leaves me with negative x squared plus one is equal to negative g of x.
02:19
Sorry about that.
02:21
Let's get rid of this one, negative g of x.
02:27
Divide by negative 1.
02:33
Get that g of x is equal to x squared minus 1.
02:42
And we're going to use that same process for a few other examples.
02:54
Let's do the same process again, but where h of x is a different function.
03:03
So we're going to take h of x, which is the square root of x minus 4 plus 5x plus 2, and we're going to substitute it into the left side of this equation.
03:21
X minus 4 plus 5x plus 2 is equal to.
03:28
And again, take what i know f of x is, and substitute it in for the f part.
03:38
So 5x plus 2.
03:41
And then we can solve for the negative g or minus g of x.
03:50
Subtract the 5x.
03:52
Subtract the 2.
03:55
Subtract the 5x, subtract the 2.
03:58
That gets rid of the f function on the right hand side.
04:05
It gets rid of those...