00:01
Hey folks, we're going to be doing some algebra with functions here.
00:03
So first we need to find f plus g, f minus g, fg and f over g, and their respective domains where these are our functions.
00:12
Oops, and i forgot to write down in part b what the functions are, but this is, so let me just fix this really quick.
00:23
And then we will get gone.
00:33
Okay, so first for part a, let's, so we have f plus g, so what are we doing here? we're literally, just adding f and g.
00:44
So this is square root 25 minus x squared plus square root x plus one.
00:52
And the domain, well, so the domain we need to make sure we don't take the square root of anything negative, right? so we certainly need x bigger than or equal to minus one so that this thing is not negative.
01:11
But we also, so we're doing 25.
01:13
Minus x squared, right? in order for that to not be negative, we also need x to be between negative and five, right? otherwise, 25 minus x squared.
01:27
If x is outside this range, x squared will be bigger than 25, and this will be negative inside there.
01:33
And so, to put this in interval notation, we want numbers bigger than or equal to negative 1, but we can't go any bigger than 5.
01:46
F minus g is the same thing.
01:50
We just put a minus sign.
02:00
And the domain is again minus 1 to 5 for the same reason.
02:14
Fg of x now is just the product.
02:27
And here we again have to be careful because you might think, oh, we can just multiply the insides together, right? inside one square root.
02:42
But that only works when the insides are not negative.
02:46
And so the domain here is actually still the same because we need both of these factors to have non -negative numbers on the inside.
02:57
So again, it's negative 1 to 5.
03:00
And so long as x is within that range, you can write this if you want as a single square root.
03:08
So long as you just need both of these things to individually be non -negative in the inside the square root...