2005 AMC 12A Problems/Problem 20
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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) | ||
| 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 | ||
