00:01
In this question, we are asked to find all discontinuities of the function f.
00:06
Note that each part of the function is continuous for all values of x.
00:11
X plus 4 is always continuous, and 1 33x plus 7 is always continuous.
00:16
So we might have, the only problem might be at the point x equals 3, because that's where the function changes its definition.
00:25
So for the function f to be continuous at x equals 3, if a function f, the limit from the left, the limit of f as x goes to 3 from the left, equals to the limit of f as x goes to 3 from the right, equals to f of 3.
00:54
If at least one of these conditions breaks, then the function is discontinuous.
01:01
So let's calculate the limits.
01:03
First, let's start with the limit from the left.
01:07
X goes to 3 from the left means that x is slightly less than 3, and that means that we are in the first case.
01:14
And we need to replace f by 1 3x plus 7...