Determine, em $\\mathbb{R}$, o dom\u00ednio das fun\u00e7\u00f5es:<\/p>\n
- \n
- $f:x\\to \\sqrt{-x}$<\/li>\n
- $g:x\\to \\sqrt{\\frac{x-3}{x-4}}$<\/li>\n
- $h:x\\to \\sqrt{-{{x}^{2}}+4x}$<\/li>\n
- $i:x\\to \\frac{\\sqrt{x-3}}{\\sqrt{x-4}}$<\/li>\n<\/ol>\nResolu\u00e7\u00e3o >><\/a><\/span><\/div><\/div>\n\n\nResolu\u00e7\u00e3o<\/b><\/span><\/p>\n
- \n
- $f:x\\to \\sqrt{-x}$\n
${{D}_{f}}=\\left\\{ x\\in \\mathbb{R}:-x\\ge 0 \\right\\}=\\mathbb{R}_{0}^{-}$.<\/p>\n
![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/11-04-2011-Ecra011-300x225.png\" "\\"Gr\u00e1fico")
<\/a><\/p>\n<\/li>\n- $g:x\\to \\sqrt{\\frac{x-3}{x-4}}$
\n\\[\\begin{array}{*{35}{l}}
\n{{D}_{g}} & = & \\left\\{ x\\in \\mathbb{R}:\\frac{x-3}{x-4}\\ge 0 \\right\\}\u00a0 \\\\
\n{} & = & \\left\\{ x\\in \\mathbb{R}:(x-3\\le 0\\wedge x-4<0)\\vee (x-3\\ge 0\\wedge x-4>0) \\right\\}\u00a0 \\\\
\n{} & = & \\left\\{ x\\in \\mathbb{R}:(x\\le 3\\wedge x<4)\\vee (x\\ge 3\\wedge x>4) \\right\\}\u00a0 \\\\
\n{} & = & \\left\\{ x\\in \\mathbb{R}:x\\le 3\\vee x>4 \\right\\}\u00a0 \\\\
\n{} & = & \\left] -\\infty ,3 \\right]\\cup \\left] 4,+\\infty\u00a0 \\right[\u00a0 \\\\
\n\\end{array}\\]![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/11-04-2011-Ecra012-300x225.png\" "\\"Gr\u00e1fico")
<\/a><\/li>\n- $h:x\\to \\sqrt{-{{x}^{2}}+4x}$\n
${{D}_{h}}=\\left\\{ x\\in \\mathbb{R}:-{{x}^{2}}+4x\\ge 0 \\right\\}=\\left\\{ x\\in \\mathbb{R}:-x(x-4)\\ge 0 \\right\\}=\\left[ 0,4 \\right]$.<\/p>\n
- $g:x\\to \\sqrt{\\frac{x-3}{x-4}}$
- $f:x\\to \\sqrt{-x}$\n
![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/11-04-2011-Ecra013-300x225.png\" "\\"Gr\u00e1fico")
<\/a><\/p>\n<\/li>\n![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/11-04-2011-Ecra014-300x225.png\" "\\"Gr\u00e1fico")
<\/a><\/p>\n<\/li>\n<\/ol>\n