{"status": "success", "data": {"description_md": "Let $f(x) = x+1, g(x) = 2x$ and let $m$ be a non-negative integer.\n\n___\n\nFind, with proof, the number of ways there are to write $4(x+m)$ as compositions of $f$ and $g$. Express your answer in terms of $m$.", "description_html": "<p>Let <span class=\"katex--inline\">f(x) = x+1, g(x) = 2x</span> and let <span class=\"katex--inline\">m</span> be a non-negative integer.</p>&#10;<hr/>&#10;<p>Find, with proof, the number of ways there are to write <span class=\"katex--inline\">4(x+m)</span> as compositions of <span class=\"katex--inline\">f</span> and <span class=\"katex--inline\">g</span>. Express your answer in terms of <span class=\"katex--inline\">m</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Mock Euclid 2025 - Problem 9 Part B", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}