00:01
All right, and this problem we're asked to show why f of x and g of x are inverses of each other.
00:10
Now, if something's an inverse, that means if we take the composite function, f of g of x, we should get an answer of x.
00:17
And if i reverse that, g of f of x, i should get an answer of x.
00:23
Both of these have to be true for them to be inverses of each other.
00:28
So let's go ahead.
00:29
We'll start with f of g of x.
00:33
And what that means is i'm going to write f of x, but in place of the x, i'm going to put g of x, which is x cubed plus one.
00:44
Now, simplifying this, this is going to give me the cubed root, and this plus one and this minus one cancel out, and that just gives me x cubed, and the cubed root of x cubed is just x...