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Problems on Absolute Values
Mika Seppälä: Problems on Absolute Values
Equations
1 |2x – 8| = 2.
Solve the following equations:
|1 – |x|| = 3.2
|1 – x| + 2|x2 – 1| = 0.3
|2 – x| + |x2 – 4| = 4.4
Mika Seppälä: Problems on Absolute Values
Inequalities
5 |3x – 7| ≤ 2.
Solve the following inequalities:
|1 – x| + |x+1| ≤ 3.6
|2 –|x|| ≤ 17
Mika Seppälä: Problems on Absolute Values
Graphs
8 f(x) = |1 – |x – 1||, -1 ≤ x ≤ 3
Sketch the graphs of the following functions on the given intervals:
g(x) = |1 – |x – 3| + |x – 1|| , 0 ≤ x ≤ 49
h(x) = ||x2 – 4| – 5|, -4 ≤ x ≤ 410
Mika Seppälä: Problems on Absolute Values
Challenge Problems
11 For which value of the parameter r the equation
|x – 2| + |x – 4| = r
has infinitely many solutions? Interpret the problem geometrically. Find these solutions.
Show that x2 + 1 ≥ 2|x| for all x.12
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