{"status": "success", "data": {"description_md": "If $f(x) = ax+b$ and $f^{-1}(x) = bx+a$ with $a$ and $b$ real, what is the value of $a+b$? \n\n$\\mathrm{(A)}\\ -2<br>\\qquad\\mathrm{(B)}\\ -1<br>\\qquad\\mathrm{(C)}\\ 0<br>\\qquad\\mathrm{(D)}\\ 1<br>\\qquad\\mathrm{(E)}\\ 2$\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>If  <span class=\"katex--inline\">f(x) = ax+b</span>  and  <span class=\"katex--inline\">f^{-1}(x) = bx+a</span>  with  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  real, what is the value of  <span class=\"katex--inline\">a+b</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ -2\\qquad\\mathrm{(B)}\\ -1\\qquad\\mathrm{(C)}\\ 0\\qquad\\mathrm{(D)}\\ 1\\qquad\\mathrm{(E)}\\ 2</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": "2004 AMC 12B Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12B_p14", "prev": "/problem/04_amc12B_p12"}}