{"status": "success", "data": {"description_md": "A [[function]] $f$ has [[domain]] $[0,2]$ and [[range]] $[0,1]$. (The notation $[a,b]$ denotes $\\{x:a \\le x \\le b \\}$.) What are the domain and range, respectively, of the function $g$ defined by $g(x)=1-f(x+1)$?\n\n$\\mathrm{(A)}\\ [-1,1],[-1,0]\\qquad\\mathrm{(B)}\\ [-1,1],[0,1]\\qquad\\textbf{(C)}\\ [0,2],[-1,0]\\qquad\\mathrm{(D)}\\ [1,3],[-1,0]\\qquad\\mathrm{(E)}\\ [1,3],[0,1]$\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>A [[function]]  <span class=\"katex--inline\">f</span>  has [[domain]]  <span class=\"katex--inline\">[0,2]</span>  and [[range]]  <span class=\"katex--inline\">[0,1]</span> . (The notation  <span class=\"katex--inline\">[a,b]</span>  denotes  <span class=\"katex--inline\">\\{x:a \\le x \\le b \\}</span> .) What are the domain and range, respectively, of the function  <span class=\"katex--inline\">g</span>  defined by  <span class=\"katex--inline\">g(x)=1-f(x+1)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ [-1,1],[-1,0]\\qquad\\mathrm{(B)}\\ [-1,1],[0,1]\\qquad\\textbf{(C)}\\ [0,2],[-1,0]\\qquad\\mathrm{(D)}\\ [1,3],[-1,0]\\qquad\\mathrm{(E)}\\ [1,3],[0,1]</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": "2008 AMC 12A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12A_p13", "prev": "/problem/08_amc12A_p11"}}