00:01
So in this problem, we're given the function for f of x and g of x.
00:03
And in part a, what we want to find is f minus g of x.
00:07
Well, remember, f minus g of x means we want to find f of x minus g of x.
00:13
Well, f of x is the first function, so that would be one over 4x squared plus three.
00:19
And g of x is our second function, the square root of 5x minus 4.
00:23
Now, there's really not much we can do to simplify here, so we can leave this as this.
00:26
So this would be our f minus g of x.
00:30
Now, the next thing you need to find is the domain.
00:32
Well, first off, i see we have a fraction.
00:35
So we just have to make sure there's no value of x that will cause our denominator to be zero.
00:39
So what we'll do is we'll set our denominator equal to zero.
00:42
So to solve for x, we'll subtract both sides by three.
00:45
So 4x squared will equal to negative 3.
00:47
We'll divide both sides by 4.
00:49
So x squared will equal to negative 3 -4s.
00:51
So to solve for x, we would then take the square of the both sides.
00:55
But we can't take the square of the negative number.
00:57
So there is no values that will cause it to be zero.
01:00
Now, we also have a radical.
01:02
Keep in mind that inside our radical has to be positive.
01:06
So now we have to make sure that what's inside our radical, in other words, our radican, the 5x minus 4, is greater than or equal to 0...