Verifique se s\u00e3o iguais as fun\u00e7\u00f5es reais de vari\u00e1vel real, f e g, assim definidas:<\/p>\n
- \n
- $\\begin{matrix}
\nf:x\\to \\sqrt{{{(-x)}^{2}}} & {} & g:x\\to \\left| x \\right|\u00a0 \\\\
\n\\end{matrix}$<\/li>\n - $\\begin{matrix}
\nf:x\\to \\sqrt{x}.\\sqrt{x} & {} & g:x\\to x\u00a0 \\\\
\n\\end{matrix}$<\/li>\n - $\\begin{matrix}
\nf:x\\to \\sqrt{x+1}.\\sqrt{x-1} & {} & g:x\\to \\sqrt{{{x}^{2}}-1}\u00a0 \\\\
\n\\end{matrix}$<\/li>\n<\/ol>\nResolu\u00e7\u00e3o >><\/a><\/span><\/div><\/div>\n\n\nResolu\u00e7\u00e3o<\/b><\/span><\/p>\n- \n
- Como\n
${{D}_{f}}={{D}_{g}}=\\mathbb{R}$,<\/p>\n
$f(x)=\\sqrt{{{(-x)}^{2}}}=\\left| x \\right|=g(x),\\forall x\\in \\mathbb{R}$<\/p>\n
e ambas as fun\u00e7\u00f5es t\u00eam o mesmo conjunto de chegada ($\\mathbb{R}$),<\/p>\n
ent\u00e3o as fun\u00e7\u00f5es f e g s\u00e3o iguais.<\/p>\n
\u00a0
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<\/a>\u00a0![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/10-04-2011-Ecra002-300x225.png\" "\\"Gr\u00e1fico")
<\/a><\/p>\n<\/li>\n- Como ${{D}_{f}}=\\mathbb{R}_{0}^{+}$ e ${{D}_{g}}=\\mathbb{R}$, ent\u00e3o as fun\u00e7\u00f5es n\u00e3o s\u00e3o iguais, pois ${{D}_{f}}\\ne {{D}_{g}}$.\n
\u00a0
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<\/a>\u00a0![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/10-04-2011-Ecra004-300x225.png\" "\\"Gr\u00e1fico")
<\/a><\/p>\n<\/li>\n- Ora,\n
${{D}_{f}}=\\left\\{ x\\in \\mathbb{R}:x+1\\ge 0\\wedge x-1\\ge 0 \\right\\}=\\left\\{ x\\in \\mathbb{R}:x\\ge -1\\wedge x\\ge 1 \\right\\}=\\left[ 1,+\\infty\u00a0 \\right[$<\/p>\n
e ${{D}_{g}}=\\left\\{ x\\in \\mathbb{R}:{{x}^{2}}-1\\ge 0 \\right\\}=\\left] -\\infty ,-1 \\right]\\cup \\left[ 1,+\\infty\u00a0 \\right[$.<\/p>\n
Logo, as fun\u00e7\u00f5es n\u00e3o s\u00e3o iguais, pois ${{D}_{f}}\\ne {{D}_{g}}$.<\/p>\n
- Como ${{D}_{f}}=\\mathbb{R}_{0}^{+}$ e ${{D}_{g}}=\\mathbb{R}$, ent\u00e3o as fun\u00e7\u00f5es n\u00e3o s\u00e3o iguais, pois ${{D}_{f}}\\ne {{D}_{g}}$.\n
- Como\n
![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/10-04-2011-Ecra005-300x225.jpg\" "\\"Gr\u00e1fico")
<\/a>\u00a0![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/10-04-2011-Ecra006-300x225.png\" "\\"Gr\u00e1fico")
<\/a><\/p>\n<\/li>\n<\/ol>\n