{"status": "success", "data": {"description_md": "The function $f$ defined by $\\displaystyle f(x)= \\frac{ax+b}{cx+d}$. where $a,b,c$ and $d$ are nonzero real numbers, has the properties $f(19)=19, f(97)=97$ and $f(f(x))=x$ for all values except $\\displaystyle \\frac{-d}{c}$. Find the unique number that is not in the range of $f$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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 function <span class=\"katex--inline\">f</span> defined by <span class=\"katex--inline\">\\displaystyle f(x)= \\frac{ax+b}{cx+d}</span>. where <span class=\"katex--inline\">a,b,c</span> and <span class=\"katex--inline\">d</span> are nonzero real numbers, has the properties <span class=\"katex--inline\">f(19)=19, f(97)=97</span> and <span class=\"katex--inline\">f(f(x))=x</span> for all values except <span class=\"katex--inline\">\\displaystyle \\frac{-d}{c}</span>. Find the unique number that is not in the range of <span class=\"katex--inline\">f</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 5, "problem_name": "1997 AIME Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/97_aime_p13", "prev": "/problem/97_aime_p11"}}