Difference between revisions of "2005 AMC 12A Problems/Problem 20"
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Revision as of 21:20, 3 July 2013
Problem
For each in
, define
Let
, and
for each integer
. For how many values of
in
is
?
Solution
For the two functions and
,we can see that as long as
is between
and
,
will be in the right domain. Therefore, we don't need to worry about the domain of
. Also, every time we change
, the final equation will be in a different form and thus we will get a different value of x. Every time we have two choices for
) and altogether we have to choose
times. Thus,
.
See Also
2005 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 19 |
Followed by Problem 21 |
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.