00:01
Here we're given a function f of x, which is equal to the square root of 2 plus x minus x squared plus 1.
00:08
And we want to find the domain and range.
00:10
So to find the domain of this, basically what we need to do is find out where this stuff inside is greater than 0.
00:16
To do that, i'm actually just going to set it equal to 0.
00:19
I'm also going to multiply by negative 1 to get x squared minus x minus 2 equals 0, just because it's easier to factor it.
00:26
And this factors into x minus 1 and x plus 1 and x minus 2.
00:33
So that gives me x equals negative 1 and 2.
00:37
Now all we have to do is just figure out where is it positive, in what interval.
00:40
So if we check a number somewhere in here, say 0, this thing is going to be positive.
00:45
So it's positive here and negative elsewhere...