9.2
Intersections, Unions, and
Compound Inequalities
Quick Check Exercises
The following exercises are similar to those in the video section. Work
these exercises on your own to test your understanding of the material.
1. Find the indicated intersection or union
(a) {a,b,c,d } ∩ {c,d ,e}
(b) {2 , 4 , 6 ,8} ∪ {4 ,8,12 ,16}
2. Graph and write interval notation for each compound inequality.
(a) −1 < 2 x + 3 < 9
(b) t − 2 < −1 or t + 2 > 7
3. For f ( x ) = x − 5 , use interval notation to write the domain of f.
9.2
Intersections, Unions, and
Compound Inequalities
Quick Check Exercise Solutions
Please check your answers against the solutions provided below.
1. Find the indicated intersection or union
(a) {a,b,c,d } ∩ {c,d ,e}
Solution:
{a,b,c,d } ∩ {c,d ,e} = {c,d }
(b) {2 , 4 , 6 ,8} ∪ {4 ,8,12 ,16}
Solution:
{2, 4,6,8} ∪ {4,8,12,16}
= {2 , 4,6 ,8,12,16}
2. Graph and write interval notation for each compound inequality.
(a) −1 < 2 x + 3 < 9
Solution: −1 < 2 x + 3 < 9
−4 < 2 x < 6
−2 < x < 3
The solution set is { x | −2 < x < 3} , or ( −2 ,3) .
(b) t − 2 < −1 or t + 2 > 7
Solution: t − 2 < −1 or t + 2 > 7
t < 1 or t > 5
The solution set is {t | t < 1} ∪ {t | t > 5} , or ( −∞ ,1) ∪ ( 5, ∞ ) .
3. For f ( x ) = x − 5 , use interval notation to write the domain of f.
Solution: f ( x ) = x − 5
x − 5 is not a real number when x − 5 is negative. Thus, the domain of f is the set
of all x-values for which x − 5 ≥ 0 . Since x − 5 ≥ 0 is equivalent to x ≥ 5 , we have
Domain of f = [5,∞ ) .