00:01
Let's talk about the continuity of the composite functions.
00:05
So if our functions f of x and g of x are continuous, then we know that the composite function is also going to be continuous.
00:16
So i'm looking at three of these, which are going to be continuous.
00:20
F and g, in 65, both f and g are polynomial, so they are both continuous, which means the continuity of the composite is also continuous.
00:31
66, again, both polynomials, both continuous, composite is continuous everywhere.
00:38
Now, in 70, x squared's a polynomial, and when i look at sign, it's continuous everywhere.
00:45
So that's also going to be continuous.
00:48
When we do the composite, it will also be continuous everywhere.
00:52
So 65, 66, and 70, the composite is going to be continuous for all values of x10.
01:01
Now let's look at the others where we do have some issues.
01:05
If we look at 67, when we put g in place of x and f, we're going to have f.
01:11
We're going to have x squared plus 5 minus 6.
01:15
And when we simplify that, we're going to get x squared minus 1...