MAT 104 Quiz 2
Friday, February 11, 2005
1. (a) Solve the inequality below and write your answer in set builder no-
tation.
3−x≥7−3x
3−x≥7−3x=⇒3+2x≥7
=⇒2x≥4
=⇒x≥2
So the solution set is
{x|x≥2}
(b) Write your answer in interval notation.
[2,∞)
(c) Indicate your solution on the number line below.
0-1-2-3-4-5 1 2 3 4 5
2. Solve the following inequality:
|2x+ 3| ≥ 3
First split this as two inequalities. Remember, this is saying that we want
the expression (2x+ 3) to live at least 3 units away from 0. To be that far
from zero, the expression can be to the right of 3 (greater than or equal
to 3), or to the left of -3 (less than or equal to -3). So we have
2x+ 3 ≥3 or 2x+ 3 ≤ −3
Solving each of these inequalities individually, we get
x≥0 or x≤ −3
3. For the function fgiven by f(x) = x2+x−3, find
(a) f(2) = (2)2+ 2 −3 = 4 + 2 −3 = 3
(b) f(−1) = (−1)2+ (−1) −3 = 1 −1−3 = −3
(c) f(a) = a2+a−3
