Difference between revisions of "2011 AMC 12A Problems/Problem 21"
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== Problem == | == Problem == | ||
| + | Let <math>f_{1}(x)=\sqrt{1-x}</math>, and for integers <math>n \geq 2</math>, let <math>f_{n}(x)=f_{n-1}(\sqrt{n^2 - x})</math>. If <math>N</math> is the largest value of <math>n</math> for which the domain of <math>f_{n}</math> is nonempty, the domain of <math>f_{N}</math> is <math>[c]</math>. What is <math>N+c</math>? | ||
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| + | <math> | ||
| + | \textbf{(A)}\ -226 \qquad | ||
| + | \textbf{(B)}\ -144 \qquad | ||
| + | \textbf{(C)}\ -20 \qquad | ||
| + | \textbf{(D)}\ 20 \qquad | ||
| + | \textbf{(E)}\ 144 </math> | ||
| + | |||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
{{AMC12 box|year=2011|num-b=20|num-a=22|ab=A}} | {{AMC12 box|year=2011|num-b=20|num-a=22|ab=A}} | ||
Revision as of 02:36, 10 February 2011
Problem
Let 
, and for integers 
, let 
. If 
is the largest value of 
for which the domain of 
is nonempty, the domain of 
is ![$[c]$](http://latex.artofproblemsolving.com/5/2/b/52bae999d8320de9922bb4da965c7d6eb93f7ed1.png)
. What is 
?
Solution
See also
| 2011 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 20 |
Followed by Problem 22 |
| 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 | |
