\nConsidere as fun\u00e7\u00f5es reais de vari\u00e1vel real $f$ e $g$ definidas por $$\\begin{matrix}
\nf(x)={{e}^{2x+1}} & {} & {} & g(x)=\\ln \\left( 3-3x \\right)\u00a0 \\\\
\n\\end{matrix}$$<\/p>\n<\/blockquote>\n
\u00ad<\/p>\n
\n- \u00a0Os dom\u00ednios das fun\u00e7\u00f5es $f$ e $g$ s\u00e3o:
\n$$\\begin{array}{*{35}{l}}
\n{{D}_{f}} & = & \\left\\{ x\\in \\mathbb{R}:\\left( 2x+1 \\right)\\in \\mathbb{R} \\right\\}\u00a0 \\\\
\n{} & = & \\mathbb{R}\u00a0 \\\\
\n\\end{array}$$
\n\\[\\begin{array}{*{35}{l}}
\n{{D}_{g}} & = & \\left\\{ x\\in \\mathbb{R}:3-3x>0 \\right\\}\u00a0 \\\\
\n{} & = & \\left] -\\infty ,1 \\right[\u00a0 \\\\
\n\\end{array}\\]
\n\u00ad<\/li>\n - Comecemos por determinar o dom\u00ednio de $f\\circ g$:\\[\\begin{array}{*{35}{l}}
\n{{D}_{f\\circ g}} & = & \\left\\{ x\\in \\mathbb{R}:x\\in {{D}_{g}}\\wedge g(x)\\in {{D}_{f}} \\right\\}\u00a0 \\\\
\n{} & = & \\left\\{ x\\in \\mathbb{R}:x<1\\wedge (\\ln \\left( 3-3x \\right))\\in \\mathbb{R} \\right\\}\u00a0 \\\\
\n{} & = & \\left\\{ x\\in \\mathbb{R}:x<1\\wedge x<1 \\right\\}\u00a0 \\\\
\n{} & = & \\left] -\\infty ,1 \\right[\u00a0 \\\\
\n\\end{array}\\]
\nOra, $$\\begin{array}{*{35}{l}}
\n(f\\circ g)(x) & = & f(g(x))\u00a0 \\\\
\n{} & = & f(\\ln \\left( 3-3x \\right))\u00a0 \\\\
\n{} & = & {{e}^{2\\times (\\ln \\left( 3-3x \\right))+1}}\u00a0 \\\\
\n{} & = & {{e}^{2\\times \\ln \\left( 3-3x \\right)}}\\times {{e}^{1}}\u00a0 \\\\
\n{} & = & {{e}^{1}}\\times {{e}^{\\ln {{\\left( 3-3x \\right)}^{2}}}}\u00a0 \\\\
\n{} & = & e\\times {{(3-3x)}^{2}}\u00a0 \\\\
\n\\end{array}$$
\nLogo: \\[\\begin{array}{*{35}{l}}
\nf\\circ g: & \\left] -\\infty ,1 \\right[\\to \\mathbb{R}\u00a0 \\\\
\n{} & x\\to e\\times {{(3-3x)}^{2}}\u00a0 \\\\
\n\\end{array}\\]<\/li>\n<\/ol>\n