Art of Problem Solving

2014 AMC 12A Problems/Problem 24: Difference between revisions

Created page with "==Problem== Let <math>f_0(x)=x+|x-100|-|x+100|</math>, and for <math>n\geq 1</math>, let <math>f_n(x)=|f_{n-1}(x)|-1</math>. For how many values of <math>x</math> is <math>f_{10..."
 
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\textbf{(D) }302\qquad
\textbf{(D) }302\qquad
\textbf{(E) }303\qquad</math>
\textbf{(E) }303\qquad</math>
==Solution==
==See Also==
{{AMC12 box|year=2014|ab=A|num-b=23|num-a=25}}
{{MAA Notice}}

Revision as of 13:37, 8 February 2014

Problem

Let $f_0(x)=x+|x-100|-|x+100|$, and for $n\geq 1$, let $f_n(x)=|f_{n-1}(x)|-1$. For how many values of $x$ is $f_{100}(x)=0$?

$\textbf{(A) }299\qquad \textbf{(B) }300\qquad \textbf{(C) }301\qquad \textbf{(D) }302\qquad \textbf{(E) }303\qquad$

Solution

See Also

2014 AMC 12A (ProblemsAnswer KeyResources)
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

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