Difference between revisions of "2014 AMC 12A Problems/Problem 24"
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\textbf{(D) }302\qquad | \textbf{(D) }302\qquad | ||
\textbf{(E) }303\qquad</math> | \textbf{(E) }303\qquad</math> | ||
| − | ==Solution== | + | ==Solution 1== |
1. Draw the graph of <math>f_0(x)</math> by dividing the domain into three parts. | 1. Draw the graph of <math>f_0(x)</math> by dividing the domain into three parts. | ||
Revision as of 18:15, 15 February 2014
Contents
Problem
Let 
, and for 
, let 
. For how many values of 
is 
?
Solution 1
1. Draw the graph of 
by dividing the domain into three parts.
2. Look at the recursive rule. Take absolute of the previous function and down by 1 to get the next function.
3. Count the x intercepts of the each function and find the pattern.
The pattern turns out to be 
solutions, and the answer is thus 
.
(Revised by Flamedragon)
Solution 2
First, notice that the recursion and the definition of require that for all such that 
, if , then is even. Now, we can do case work on to find which values of (such that ) make even. The answer comes out to be all the even values of in the range . So, the answer is 
.
See Also
| 2014 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 23 |
Followed by Problem 25 |
| 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. 
