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Fisa de lucru;functii, notiuni introductive, proprietatiClasa a IX-aI.Completatipespatiilepunctateraspunsurilecorecte:1) Daca A= 1,2 si B= π, π, π atunci nr. de functii definite pe A cu valori in B este................2) Fie f:RβR, f(x)=3x-2.Atunci, f(3)=............. si f(x+5)=.................3) Fie f:RβR, f(x-2)=-3x-5; atunci f(2)=.............4) Daca g:{0,1,2}βR, g(x)=3x+1, atunci Im g=.............5) Domeniulmaxim de definitie al functiei f(x)=π₯+53βπ₯este.................6) Domeniulmaxim de definitie al functiei h(x)= 2π₯ β 8 este.......................7) Domeniul de definitie A al functiei f:Aβ{-7,-5,-1,1,4} , f(x)=2x-3 este....................8) Domeniulmaxim de definitie al functiei h(x)=π₯π₯2+5este................................9) Domeniul de maxim de definitie al functiei f(x)= π₯ β 6 este..................II.Rezolvati integralsubiecteleurmatoare:1.Se da functia f:{-2;-1;0;1;2;3;4}βR, f(x)=ππ₯ β 1 ; π₯ < 1π₯ + π ; π₯ β₯ 1.Aflati a stiind ca f(2)=4, apoi determinatiimaginealui f.2. Se daufunctiilef,g:RβR, f(x)= π₯ -1 si g(x)= π₯ β 1 .Stabiliti daca f=g3. Stabilitidaca f:NβQ, f(x)= π₯defineste o functie.4. a) Se considerafunctiaπ: π β π , π π₯ = 3π₯ β 4. ππ π π πππππ’πππ§π π 1 + π 2 + β―+ π 100 .b) Se considerafunctiaπ: π β π , π π₯ = 2 β π₯.Sa se calculezeπ 0 β π 1 β β― β π 20 .5. Sa se determinefunctia f: π β π , π π₯ = ππ₯ + π , cu a si b numererealepentru care π 1 + π 2 + π 3 == 6π + 2π π π π 4 = 8.6. Se considerafunctiileπ, π: π β π , π π₯ = ππ₯ + π, π π₯ = ππ₯ + π.Demonstratica, dacaπ 2 = π 2 π ππ 5 = π 5 ,atunci f=g.7.Studiatidaca exista o functie al careigrafic sa continapuncteleA(1,-2), B(3,1), C(1,4) si D(3,7).8. Studiati care dintrefunctiileurmatoaresunt pare sauimpare :a) π: π β π , π π₯ = π₯2 + 2; π) π: π β π , π π₯ = 1 β π₯ + π₯2; π) π: π β π , π π₯ =2π₯3+4π₯2; d) f: β2,+β β π ,f π₯ = 3π₯2 + 15.9. Studiatimonotoniafunctiilorurmatoare :a) f :RβR, π π₯ = 3π₯ β 4; π)π: π β π , π π₯ = β2π₯ + 4;c) studiatimonotonia lui f pe(ββ, 0) π πππ (0,+β)pentru f(x)=1π₯, apoipentru g(x)=1π₯2 .10. Studiatimarginirea( nemarginirea) functiilor :a) f :[-2,4]β π , π π₯ = 2π₯ β 4; b) f:[-2,+β) β π , π π₯ = 3π₯ + 1; f:(0,2)β π , π π₯ = β4π₯ + 3 ..