Union and intersection of intervals
1 answer:
Answer:
Step-by-step explanation:
Union and intersection of intervals
We are given the following intervals:
We need to find the union and the intersection of the intervals.
Both intervals are represented in the number line as shown in the figure below.
The union of intervals is the set of elements that belong to any of the intervals.
Since both intervals have no common area:
The intersection of intervals is the set of elements that belong to all the intervals.
As pointed above, there is no common area, thus the intersection is empty
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<h3>Answers:</h3>
- g(-1) = -1
- g(1) = -3/2
- g(5) = -7/2
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Explanation:
The piecewise function g(x) is defined based on what the input is.
- If the input x is less than -2, then g(x) = 2
- Or if
then g(x) = -(x-1)^2+3
- Or if
then g(x) = (-1/2)x-1
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In the case of g(-1), we have x = -1 which makes true.
So we'll use the second piece
g(x) = -(x-1)^2+3
g(-1) = -(-1-1)^2+3
g(-1) = -(-2)^2+3
g(-1) = -4+3
g(-1) = -1
----------------
For g(1), we have x = 1 which makes true
We'll use the third piece
g(x) = (-1/2)x-1
g(1) = (-1/2)*1 - 1
g(1) = -1/2 - 1
g(1) = -1/2 - 2/2
g(1) = -3/2
-----------------
For g(5), we have x = 5 which makes true
g(x) = (-1/2)x-1
g(5) = (-1/2)*5-1
g(5) = -5/2 - 1
g(5) = -5/2 - 2/2
g(5) = -7/2