Difference between revisions of "2003 AMC 12A Problems/Problem 6"
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Therefore the statement that is not true is <math>\boxed{\mathrm{(C)}\ x\heartsuit 0=x\ \text{for all}\ x}</math> | Therefore the statement that is not true is <math>\boxed{\mathrm{(C)}\ x\heartsuit 0=x\ \text{for all}\ x}</math> | ||
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+ | == Video Solution == | ||
+ | |||
+ | https://www.youtube.com/watch?v=d-IRsaIUdDA ~David | ||
== See Also == | == See Also == |
Revision as of 21:44, 19 July 2023
- The following problem is from both the 2003 AMC 12A #6 and 2003 AMC 10A #6, so both problems redirect to this page.
Contents
Problem
Define to be
for all real numbers
and
. Which of the following statements is not true?
for all
and
for all
and
for all
for all
if
Solution
Examining statement C:
when
, but statement C says that it does for all
.
Therefore the statement that is not true is
Video Solution
https://www.youtube.com/watch?v=d-IRsaIUdDA ~David
See Also
2003 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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 10 Problems and Solutions |
2003 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 5 |
Followed by Problem 7 |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.