00:01
In this question, we say we want to find x1 and x2 where this function f of x is discontinuous if they exist.
00:07
We're going to classify each discontinuities, and if there are any extra blanks, we'll enter d &e.
00:14
So where am i concerned about the continuity? i'm concerned about the continuity, really, only at x equals zero at this time.
00:24
Each of these functions, 9e to the negative 5x and 3x plus 9, they are each continuing.
00:31
On their entire domains.
00:33
There are no discontinuities as the domain of each of those functions on their own is all real numbers.
00:42
And so my concern is continuity at x equals zero.
00:51
What do i have to determine to see if we are continuous at x equals zero? well, i have to look at the limit as x approaches zero from the left of this function and the limit as x approaches zero.
01:06
And the limit as x approaches is zero from the right of this function.
01:13
Now, if x is approaching zero from the left, which piece of function am i using? i'm using this top piece of function, since that's where x is less than zero.
01:26
I'm looking at the limit as x approaches zero from the left of 9e to the negative 5x.
01:33
Now, how do i evaluate that limit? i try to plug in.
01:37
I plug in zero for x, and when i do, i'm getting 9e to the 0 power, e to the 0 is 1, 9 times 1 is 9.
01:51
So my limit as x approaches 0 from the left of this function is 9...