Absolute Value and Order
GRE · Flashcards · Recall
GRE · FLASHCARDS
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QUESTION
What is the definition of absolute value
∣
x
∣
|x|
∣
x
∣
written as a piecewise function?
QUESTION
What inequality is equivalent to
∣
x
∣
≤
a
|x|\le a
∣
x
∣
≤
a
for
a
>
0
a>0
a
>
0
?
QUESTION
What is the smallest possible value of
∣
x
∣
|x|
∣
x
∣
for real
x
x
x
, and when does it occur?
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ANSWER
Minimum is
0
0
0
, occurring at
x
=
0
x=0
x
=
0
. The absolute value |x| is always non-negative, reaching its minimum of 0 only when x=0.
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