{"status": "success", "data": {"description_md": "The function $f$ has the property that for each real number $x$ in its domain, $1/x$ is also in its domain and \n\n$f(x)+f\\left(\\frac{1}{x}\\right)=x$<br>What is the largest set of real numbers that can be in the domain of $f$?\n\n$\\mathrm{(A) \\ } \\{x|x\\ne 0\\}\\qquad \\mathrm{(B) \\ } \\{x|x<0\\}\\qquad \\mathrm{(C) \\ } \\{x|x>0\\}\\qquad \\mathrm{(D) \\ } \\{x|x\\ne -1\\;$ $\\mathrm{and}\\; x\\ne 0\\;\\mathrm{and}\\; x\\ne 1\\}\\qquad \\mathrm{(E) \\ }  \\{-1,1\\}$\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 function  <span class=\"katex--inline\">f</span>  has the property that for each real number  <span class=\"katex--inline\">x</span>  in its domain,  <span class=\"katex--inline\">1/x</span>  is also in its domain and</p>&#10;<p> <span class=\"katex--inline\">f(x)+f\\left(\\frac{1}{x}\\right)=x</span> <br/>What is the largest set of real numbers that can be in the domain of  <span class=\"katex--inline\">f</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\{x|x\\ne 0\\}\\qquad \\mathrm{(B) \\ } \\{x|x&lt;0\\}\\qquad \\mathrm{(C) \\ } \\{x|x&gt;0\\}\\qquad \\mathrm{(D) \\ } \\{x|x\\ne -1\\;</span>   <span class=\"katex--inline\">\\mathrm{and}\\; x\\ne 0\\;\\mathrm{and}\\; x\\ne 1\\}\\qquad \\mathrm{(E) \\ }  \\{-1,1\\}</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": "2006 AMC 12A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc12A_p19", "prev": "/problem/06_amc12A_p17"}}