Chapter 3 Inequalities in one Variable

Section 3.4 Final Test

3.4.1 Final Test Module 3

This is a test for submission:
  • Unlike open exercises, no hints for formulating mathematical expressions are provided.
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Exercise 3.4.1
Find the value of the parameter α such that the inequality 2 x2 x-α has exactly one solution:
  1. The parameter value is α = .
  2. In this case x =
    is the only solution of the inequality.

Exercise 3.4.2
Find an absolute value function g(x) describing the following graph as easy as possible.

Graph of the function g(x).
Try to find a representation of the form g(x)=|x+a|+bx+c. The kink in the graph indicates how the absolute value term looks like.
  1. Find the solution set of the inequality g(x)x by means of the graph.
    The solution set is L = .
  2. g(x) =
    Absolute values can be entered in the form betrag(x-a) or abs(x-a).

Exercise 3.4.3
Which positive real numbers x satisfy the following inequalities?
  1. |3x-6|x+2 has the solution set L =
    (written as an interval).
  2. x+1 x-1 2 has the solution set L =
    (written as an interval).
Enter open intervals in the form (3;5), closed intervals in the form [3;5]. Infinity can be entered a a word or shortly a infty. Do not use notation ]a;b[ for open intervals. Sets can be entered by listing the elements {1;2;3}. For the set brackets enter AltGr+7 or AltGr+0, respectively.


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