Answer:
[-7, 1] ∪ [2, 9)
Explanation:
You want to simplify the interval expression [-7, -3] ∪ (-3, 1] ∪ [2, 4] ∪ [4, 9).
Intervals
The first two intervals of your expression can be written using inequality symbols as ...
-7 ≤ x ≤ -3 ∪ -3 < x ≤ 1
You will notice that points less than -3 are included, as are points greater than -3. Also, the point -3 is included. This means the interval is continuous a the point -3, so there need not be a break there:
= -7 ≤ x ≤ 1 or [-7, 1]
Similarly, the last pair of intervals includes points less than 4, greater than 4, and the value 4 itself. There is no break in the domain at x=4, so those intervals can be combined to ...
= 2 ≤ x < 9 or [2, 9)
Your simplified interval notation is [-7, 1] ∪ [2, 9).
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Additional comment
Another way to look at it is that there is only a break in the domain if you have to lift your pencil when you draw the domain on a number line.
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