Domaine de définition

Déterminer le domaine de définition

1) "CE : "(x^2)-4 x+3≥0
({{x,     , 1,     , 3,     }, {(x^2)-4 x+3, +, 0, -, 0, +}})
 dom f= "\!\(TraditionalForm\`\(TraditionalForm\`\"\\[LongLeftArrow], \\!\\(TraditionalForm\\`1\\)]\"\)\) ⋃ \!\(TraditionalForm\`\(TraditionalForm\`\"[\\!\\(TraditionalForm\\`3\\), \\[LongRightArrow]\"\)\)"

2) "CE : "4-9 (x^2)≠0

dom f= "\!\(TraditionalForm\`\*TagBox[\"ℝ\", Function[List[], Reals]]\) \\ {\!\(TraditionalForm\`\(-\(\(2\/3\)\)\)\),\!\(TraditionalForm\`2\/3\)}"

3) "CE : "3 (x^2)+5 x-2≠0
dom f= "\!\(TraditionalForm\`\*TagBox[\"ℝ\", Function[List[], Reals]]\) \\ {\!\(TraditionalForm\`\(-2\)\),\!\(TraditionalForm\`1\/3\)}"

4) "CE : "2 (x^3)-(x^2)-7 x+6≠0
On trouve facilement que 2 (x^3)-(x^2)-7 x+6 s’annule pour x=1. On divise donc par x-1
Ce qui donne 2 (x^3)-(x^2)-7 x+6=(x-1)(2(x^2)+x-6)

dom f= "\!\(\*FormBox[TagBox[\"ℝ\",
Function[{}, Reals]],
TraditionalForm]\) \\ {-2,1,(3/2)}"

5) "CE : "((2 (x^2)-1)/(x+3))≥0
({{x,     , -3,     , ((-(Sqrt[2]))/2),     , ((Sqrt[2])/2),     }, {2 (x^2)-1, +, +, +, 0, -, 0, +}, {x+3, -, 0, +, +, +, +, +}, {((2 (x^2)-1)/(x+3)), -, |, +, 0, -, 0, +}})

dom f= ]-3,((-(Sqrt[2]))/2)] ⋃ [((Sqrt[2])/2),⟶

6) "CE : "4 x-(x^2)>0
({{x,     , 0,     , 4,     }, {4 x-(x^2), -, 0, +, 0, -}})

dom f= "]\!\(TraditionalForm\`0\), \!\(TraditionalForm\`4\)["

7) "CE : "({{{, ({{2 x+6≥0, ⟺ x∈[-3,⟶ }, {(x^2)-4≥0,  ⟺ x∈ ←,-2] ⋃ [2,->}})}})
({{x,     , -2,     , 2,     }, {(x^2)-4, +, 0, -, 0, +}})

dom f = "\!\(TraditionalForm\`\(TraditionalForm\`\"[\\!\\(TraditionalForm\\`\\(-3\\)\\), \\!\\(TraditionalForm\\`\\(-2\\)\\)]\"\)\) ⋃ \!\(TraditionalForm\`\(TraditionalForm\`\"[\\!\\(TraditionalForm\\`2\\), \\[LongRightArrow]\"\)\)"

8) "CE : "({{{, ({{3x+1≥0, ⟺ x∈[((-1)/3),⟶ }, {x-5≠0,  ⟺ x≠ 5}})}})

dom f= [((-1)/3),5[ ⋃ ]5,⟶

9) "CE : "({{{, ({{x+2≥0, ⟺ x∈[-2,⟶ }, {4-3x>0,  ⟺ x∈⟵,(4/3)[}})}})

dom f= [-2,(4/3) [

10) "CE : "x+3≠0

dom f = ℝ \ {-3}

il n’y a pas de CE sur la racine cubique !