Answer:
[tex]1\leq x <5[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The domain of a function is the set of all possible values of x
The domain of the line with negative slope is the interval [1,3)
The domain of the line with slope equal to zero (horizontal line ) is the interval [3,5)
so
The domain of the piece-wise function is the interval [1,5)
[tex]1\leq x <5[/tex]
The value of x=1 is included in the domain set
The value of x=5 is not included in the domain set
