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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Find the value of the parameter

α

such that the inequality

2 x^{2} \leq x - α

has exactly one solution:

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 | + b x + c

. The kink in the graph indicates how the absolute value term looks like.

Find the solution set of the inequality $g (x) \leq x$ by means of the graph.
The solution set is $L$ $=$ .
$g (x)$ $=$
.
Absolute values can be entered in the form betrag(x-a) or abs(x-a).

Which positive real numbers

x

satisfy the following inequalities?

$| 3 x - 6 | \leq x + 2$ has the solution set $L$ $=$
(written as an interval).
$\frac{x + 1}{x - 1} \geq 2$ 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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