{"status": "success", "data": {"description_md": "The graph of the function $f$ is shown below. How many solutions does the equation $f(f(x))=6$ have? <br><center><img class=\"problem-image\" alt='[asy] size(200); 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(\"$x$\",-7.5,7,Ticks(xticks),EndArrow(6)); yaxis(\"$y$\",-6.5,7,Ticks(yticks),EndArrow(6)); [/asy]' class=\"latexcenter\" height=\"305\" src=\"https://latex.artofproblemsolving.com/d/8/e/d8ea42d74287fb95665640e991c92aa37ba2c70f.png\" width=\"335\"/></center>\n\n$\\text{(A) }2<br>\\qquad<br>\\text{(B) }4<br>\\qquad<br>\\text{(C) }5<br>\\qquad<br>\\text{(D) }6<br>\\qquad<br>\\text{(E) }7$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>The graph of the function  <span class=\"katex--inline\">f</span>  is shown below. How many solutions does the equation  <span class=\"katex--inline\">f(f(x))=6</span>  have? <br/><center><img class=\"latexcenter\" alt=\"[asy] size(200); 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(&#34;(-7, -4)&#34;,P1); dot(&#34;(-2, 6)&#34;,P2,LeftSide); dot(&#34;(1, 6)&#34;,P4); dot(&#34;(5, -6)&#34;,P5);  xaxis(&#34;$x$&#34;,-7.5,7,Ticks(xticks),EndArrow(6)); yaxis(&#34;$y$&#34;,-6.5,7,Ticks(yticks),EndArrow(6)); [/asy]\" height=\"305\" src=\"https://latex.artofproblemsolving.com/d/8/e/d8ea42d74287fb95665640e991c92aa37ba2c70f.png\" width=\"335\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\text{(A) }2\\qquad\\text{(B) }4\\qquad\\text{(C) }5\\qquad\\text{(D) }6\\qquad\\text{(E) }7</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2002 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12A_p20", "prev": "/problem/02_amc12A_p18"}}