00:01
Okay, so we have this function f, which is defined a piecewise as followed.
00:04
For x greater than are equal to 2, we have that f of x is a squared x minus 2a.
00:09
And for x less than 2, we have that f of x is equal to 12.
00:13
So notice that, so we want to find the value of a such that this is continuous for every x.
00:18
So notice that for x less than 2, f of x is 12, which is a continuous function.
00:23
It's just a constant function.
00:24
So it's already continuous for x less than 2.
00:27
For x greater than two we have the f of x is this function which is continuous so the only possible point where we don't have a continuity is that x equals two because these functions might not match up there may be some jump going from 12 to this function here when we go to x equals two so what we want to find is a such that f of two is equal to the limit as x tends to of f of x so f of two on one hand is two a squared minus two a and the limit from the right of f of x as x goes to two so the limit from the right so if x goes to two from the positive side of f of x is 12 so we want these two things to be equal so we want two a squared minus two a to be equal to 12 so now all we need to do is solve for a.
01:28
So firstly, let's divide everything by two.
01:30
We get a squared minus a equals six...