MathDB
f(f(x))=6

Source:

March 27, 2008
functionLaTeXspeedospiky

Problem Statement

The graph of the function f f is shown below. How many solutions does the equation f(f(x)) \equal{} 6 have? [asy]size(220); defaultpen(fontsize(10pt)+linewidth(.8pt)); dotfactor=4;
pair P1=(-7,-4), P2=(-2,6), P3=(0,0), P4=(1,6), P5=(5,-6); real[] xticks={-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6}; real[] yticks={-6,-5,-4,-3,-2,-1,1,2,3,4,5,6};
draw(P1--P2--P3--P4--P5);
dot("(-7, -4)",P1); dot("(-2, 6)",P2,LeftSide); dot("(1, 6)",P4); dot("(5, -6)",P5);
xaxis("xx",-7.5,7,Ticks(xticks),EndArrow(6)); yaxis("yy",-6.5,7,Ticks(yticks),EndArrow(6));[/asy]<spanclass=latexbold>(A)</span> 2<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 5<spanclass=latexbold>(D)</span> 6<spanclass=latexbold>(E)</span> 7 <span class='latex-bold'>(A)</span>\ 2 \qquad <span class='latex-bold'>(B)</span>\ 4 \qquad <span class='latex-bold'>(C)</span>\ 5 \qquad <span class='latex-bold'>(D)</span>\ 6 \qquad <span class='latex-bold'>(E)</span>\ 7