00:01
You're given the functions for f of x and g of x, you want to find f plus g, f minus g, f times g, and f divided by g, as well as their domains.
00:09
Well, it looks like you got f plus g of x correct as well as this domain.
00:12
So i'm going to skip over that.
00:14
So next we're going to do f minus g.
00:16
Well, remember, that means we have to take our f function, which is three minus x squared, and then we're going to subtract it by our g function, which is x squared minus four.
00:25
Now, it's really important when you do this that you put these expressions in parentheses because this minus x, minus sign, it's going to need to be distributed to both terms.
00:33
So the first two terms are all set, three minus x squared.
00:37
But then the x squared for the next term will become negative x squared, and the negative four we become positive four.
00:43
So now we can go ahead and combine our late terms.
00:46
Well, first, we have three plus four, which is equal to seven.
00:49
And then we have negative x squared minus x squared, which is negative two x squared.
00:54
So this would be our expression for f minus g.
00:57
Now we need to find a domain.
00:59
Well, as you can see, we have a polynomial function, and the domain for every polynomial function is all real numbers.
01:05
So your domain in this case, just like with f plus g of x, will be from negative infinity to positive infinity.
01:11
All right, next, let's go ahead and find f times g.
01:14
So i'll call this number two.
01:16
Well, in this case, we're going to need to multiply the two functions together.
01:20
So we're going to take 3 minus x squared, and we're going to multiply this by x squared minus 4.
01:25
So, to simplify, we're going to use the distributed property.
01:29
So first, we'll distribute the 3.
01:31
3 times x squared is 3x squared.
01:33
Then we have 3 times negative 4, which is negative 12.
01:37
Now we'll distribute the negative x squared.
01:39
Well, negative x squared times x squared is negative x to the 4 power.
01:43
And negative x squared times negative 4 is positive 4x squared...