Difference between revisions of "2004 AMC 12A Problems/Problem 16"
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~MRENTHUSIASM (Reconstruction) | ~MRENTHUSIASM (Reconstruction) | ||
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+ | ==Video Solution (Logical Thinking)== | ||
+ | https://youtu.be/46c-VN1QzWk | ||
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+ | ~Education, the Study of Everything | ||
== See also == | == See also == |
Revision as of 21:23, 26 October 2022
Problem
The set of all real numbers for which
is defined is . What is the value of
?
Solution
For all real numbers and
such that
note that:
is defined if and only if
if and only if
Therefore, we have
from which
~Azjps (Fundamental Logic)
~MRENTHUSIASM (Reconstruction)
Video Solution (Logical Thinking)
~Education, the Study of Everything
See also
2004 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 15 |
Followed by Problem 17 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |