If the domain of the function y = 3 / (1-x) is known to be (negative infinity, 1] u [4,7), then the domain of the function is I don't understand at all

If the domain of the function y = 3 / (1-x) is known to be (negative infinity, 1] u [4,7), then the domain of the function is I don't understand at all

Functions increase monotonically on (negative infinity, 1), (1, positive infinity) respectively
So you can directly substitute it into the endpoint of the domain
On (negative infinity, 1) interval, the range is (0, positive infinity)
On the interval [4,7], the range is [- 1, - 1 / 2)
So the total range is [- 1, - 1 / 2) U (0, positive infinity)
In addition, you write the value of 1, where is the open interval? That is, you can't take x = 1