2023年新高考地区数学名校地市选填压轴题好题汇编（十四）（解析）

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2023
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10ᦑ┵P-ABCḄḄᨬᜧ3,¬Uᨬᜧ34i/lov=4ᦑ⌱C.15.(2022.ÀÁÂᜧ▬+▤)Æᦪ/(x)Ḅ89ÈR,/(x+l)+,“x-l)=2,/(x+2)ᏔÆᦪ/(0)=0,ᑣ()A.109B.110C.IllD.112ூ%ᫀ௃Cூ(᪆௃ᵫ/(x+l)+/(x_l)=2,;஻x+2)+஻x)=2,BP/(x+2)=2-/(x),ᡠg/(x+4)=2—/(x+2)=2-[2—஻x)]=/(x),ᡠgÆᦪ/(x)ḄᕜÌ4,Í/(x+2)ᏔÆᦪᑣ஻-x+2)Î(x+2),ᡠgÏ(%Ð(4oxᵨ(oÒᡠgÆᦪ“X)ÓᏔÆᦪÍ“x+l)+/(x-1)=2,ᡠg“1Ôব=2,஻2)+஻4)=2,ᡠg/(1)+஻2)+/ব+/ভ=4,Í/(1)+/(T)=2,ᓽ2/(])=2,ᡠg=Í/•(0)+஻2)=2,/(0)=0,.•"2)=2,ᡠgX஻%)=[7(1)+஻2)+/(3)+/(4)]X27+஻1)+—2)=4X27+1+2=111,ᦑ⌱C.16.(2022•ÀÁÂᜧ▬+▤)a=5,6=15(ln4—ln3),c=16(ln5-ln4),ᑣ()A.a2.5»—<2.5,e>|—,:.a>b,

11ÛÜ஺ÝCÛẑ5253125<1,26214433.\161n—<151n—,ᓽ:.ch>cB.b>c>aC.a>c>bD.c>a>bூ%ᫀ௃Bூ(᪆௃êÆᦪf(x)=e'+■ᑣᏔÆᦪxNO/'(x)=e'—}20,ᡠg஻x)ᙠ(-8,0)ªᓫí⌴Aᙠ(0,+«)ªᓫí⌴ïbsinic#tan2<-11>-cos3>k>sin1>0ña=/(sinl),b=/(tan2)=/(-tan2),c=/(cos3)=/(-cos3),ᡠgò>c>a.ᦑ⌱B.18.(2022ÀÁ•áâãä+▤)ê89ᙠRªḄ᜻ÆᦪxNO,/(Ò=/,ô=/(x2)N4/(x)Ḅ(õ()A.(YO,0]U[4,e)B.[0,4]C.(^»,0]kj[2,+oo)D.[0,2]ூ%ᫀ௃Cூ(᪆௃᪷÷⚪ùxWO/(ú=/ᡠgf(x)ᙠ[0,+<»)ªïÆᦪ,b/(x)89ᙠRªḄ᜻Æᦪ,ᡠg“X)ᙠRªïÆᦪ/bû20,ᡠg(*)=/f-1ᡠg/)=/ಘᡠgô=/(/””(Ò:ᓄ'f(x),

122ᡠgªZx,(;x40ᡈxN2,2ᡠ/)".”Ḅ(7>,0]32)ᦑ⌱Cஹ"⌱⚪19.(2023•()(*+,-./01.2▤456)78஻x):;<=(>8,+MḄ᜻Cᦪ/(x+1):ᏔCᦪFGxe(O,l]K/(x)=-x(x-2),ᑣ()A./(x):ᕜQ2ḄCᦪB./(2019)+/(2020)=-1C.f(x)ḄT=[-1,1]D./(x)ḄWXYZ[y=8sxᙠ(0,2ᐔ)`ᨵ4cdeூgᫀ௃BCDூ᪆௃᪷l⚪mnoA,“X)R`Ḅ᜻Cᦪ/(x+1)ᏔCᦪᡠfMWXᐵox=1nt/(2+x)=/(-%)=-/(%)ᓽ/(x+4)=-/(x+2)=/(x)ᑣ/(x):ᕜQ4ḄᕜQCᦪA┯xynoB,/(x);<=RḄ᜻Cᦪᑣf(0)=0,/(x):ᕜQ4ḄᕜQCᦪᑣ/(2020)=/(0)=0yGx«0,l]K/(x)=-x(x-2),{IJ/প=—1x(1—2)=1,ᑣ“2019)="T+2020)=/(-1)=-/প=-1,ᑣ/(2019)+/(2020)=-1yᦑB.noC,Gx40,1]K/(x)=-x(x-2),Kᨵ0V/(x)41,ᵫ/?`Ḅ᜻Cᦪᑣxe[-l,0)K/(())=(),Cᦪᐵox=lntᡠCᦪ/(x)ḄT=I-3].ᦑC.noD,•.•/(0)=0,Fxw(O,l]K/(x)=-x(x-2),xeL0,lJ,/(x)=-x(x-2),xe[1,2J,2-xe[0,1J,/(x)=/(2-x)=-x(x-2),xe[0,2]J(x)=-x(x-2),,."(x):᜻CᦪX€[-2,0]J(x)=x(x+2),,."(x)ḄᕜQ4,xe[2,4],/(x)=(x-2)(x-4),

13/.XG[4,6J,f(x)=-(x-4)(x-6),:.XG[6,2^r],/(x)=(x-6)(x-8),g(x)=/(x)-cosx,Gxw[0,2],g(x)=-x2+2x-cosx,g'(x)=-2x+2+sinx,஻(x)=g'(x\h'(x)=-2+cosx<0ᙠ[0,2]ឤᡂ஻(x)ᙠ[0,2]ᓫ⌴ᓽg'(x)ᙠ[0,2]ᓫ⌴Fg'(l)=sin1>0,g'(2)=-2+sin2<0,ᙠ/e(l,2),g(x())=0,xe(O,Xo),g(x)>O,g(x)ᓫ⌴xe(x,2),g'(x)O,g(x)>g(l)>0,g(2)=-cos2>0,oᡠg(x)ᙠ(O,x)ᨵ>¡eᙠ(᳝),2)£ᨵ¡eoᓽxe(0,2],“X)ḄWXYZ[)=8sxᨵ1cdeGxe[2,4]Kg(x)=/(x)-cosx=x2-6x+8-cosx,{ijg'(x)=2x-6+sinx,஻(x)=g'(x)=2x-6+sinx,ᑣh'(x)=2+cosx>0,ᡠg'(x)ᙠ[2,4]`ᓫ⌴Fg<3)=sin3X),g<2)=-2+sin2<0,ᡠᙠ>Ḅᓛe[2,3]u[2,4],§¨g[x)=0,ᡠxe(2,xj,g[x)<0,g(x)ᙠ(2,xJᓫ⌴xe(%,4),g0,g(x)ᙠ(©4)ᓫ⌴,gব=T-cos3<0,ᡠg(xj0,g(4)=-cos4>0,ᡠg(x)ᙠ(2,©)`ᨵ>c>Ḅ¡eᙠ(«4)`ᨵ>Ḅ¡eᡠGxe[Z4]K/(x)ḄWXYZ[y=cosxᨵ2cde,Gxe[4,6]Kxe[0,2],.f(x)ḄWXYZ[®=cosxᨵ1cde,Gx£[6,2%],/(x)=(x—6)(%-8)<0,y=cosx>0,/(X)ḄWXYZ[y=cosx£ᨵdeᡠ“X)ḄWXYZ[y=cosxᙠ(0,2ᐔ)`ᨵ4cdeᦑDyᦑ⌱BCD.20.°2022()±ᵪ᜜´µ.0.2▤456¶;<ᙠR`ḄCᦪ/°X¶·¸

14f(x+y)f(x-y)=f2(x)-f2(y),F“1)x0,ᑣ¹ᑡ»¼Ḅ:()A./(X)᜻CᦪB.஻x)Ḅ᪆>C.½/(x):ᕜQTḄCᦪᑣTHID.½x¾0K/(%)¾0,ᑣ:R`ḄCᦪூgᫀ௃ACDூ᪆௃¿஻x+y)/(x—y)=r(x)—/2(y),Àx=r=o,Á¨஻0)/(0)=/(0)-r(0),¨/(0)=0,ÂÀx=0,ᡠf(y)/(>y)=/2(o)-Ã(Ä,ᓽಔ)=—ᱏÄᡠ”—y)=—/(y),ᡠ“X)᜻CᦪᦑA;ÀC(x)=kx(k>0),ᑣÃপ-/2(È)=42/>É2y2=2232_y2),f(X+y)f(x-y)=k(x+y).k(x-y)=k\x2-y2),·¸/(x+y)/(x-y)=/(x)>Ã(y),ᦑ஻x)Ḅ᪆>ᓽB┯xy½஻x):ᕜQTḄCᦪᑣ/(x+7)=/(x),ᡠ஻T)=/(O)/পË0,ᡠTwl,ᦑCy¿Gx>0K/(x)>0,ᡠGx<0K—x>0,ᑣf(x)=-/(—x)<0,ÌmḄÍ,ᵯ«0,+»),FÐX2ᑣ஻᳝+Ñ2¶/°%>9¶=ð¶-ðҶ=Ó/°ᓰ¶>/°஽¶ÖÓ஻%¶+/°*2¶Ö,ᡠ«).஻/):Ù▾Û¿Ü€(0,ᓝR),FÂÞ2,ᡠÂ_஽Ð0/°^+X2¶¾0,/°AÖ¶¾0,/°w¶¾0,/°᳝_2¶Ð0,ᡠ/(%)-/(ß)Ð஺ᓽ஻á)Ð/(%),ᡠ“X)ᙠ(0,+8)`ᓫ⌴ᑣ“X)ᙠ(-8,0)`ᓫ⌴"0)=0,FGx¾0K/(ľ0,GxÐ0Kᑣf(x)Ð0,ᡠ஻x):R`ḄCᦪᦑDᦑ⌱ACD21.(2022()âᓭäᜧ▬0ᓭçèé.0.2▤456)78Cᦪ/(x)=lgx,ᑣ()A."2),/(ê)“5)ᡂìᦪᑡB./(2),“4),஻8)ᡂìᦪᑡC./(2),/(12),஻72)ᡂíᦪᑡD.42),/(4),“16)ᡂíᦪᑡூgᫀ௃ABD

15ூ᪆௃A/ফ+/(5)=lg2+lg5=l,2/(>/i0)=21g5/i0=21gl05=l-ᑣ/ফ+f(5)=2f(ï),ᵫì0⚗Ḅñᵨ8஻2)ஹ/(ó)ஹ”5)ᡂìᦪᑡᡠAyB/(2)=lg2,/(4)=lg4=21g2,/(8)=lg8=31g2,ᑣ/(2)+/(8)=2/(4),ᵫì0⚗Ḅñᵨ8/(2)ஹ/(4)ஹ/(8)ᡂìᦪᑡᡠByC/(2)+/(72)=lgl44=21gl2=2/(12),2/(12)=21gl2=lgl44,ᑣ”2),/(12),f(72)ᡂìᦪᑡ,஻2ᱏ/(12),ᡠC┯xyD஻2)=lg2,஻4)=lg4=21g2,஻16)=lgl6=41g2,ᑣ"(4)f=/(2)/(16),ᵫí0⚗Ḅñᵨ8,fফஹ“4)ஹ/(16)ᡂíᦪᑡᡠD.ᦑ⌱ABD.22.(2022()âᓭäᜧ▬0ᓭçèé.0.2▤456)78ᓰ,2ᑖõ:Cᦪ/(x)=e'+x-2ög(x)=lnx+x-2Ḅ¡eᑣ()A.x,+x=2B.eX|+lrLr=222C.xx>—D.x+xy<32ூgᫀ௃ABDூ᪆௃¿÷஽ᑖõ:Cᦪf(x)=e'+x-2,g(x)=lnx+x-2Ḅ¡eᡠ᮱=2-᜜C(l,l),¿Cᦪ)=஺'öy=lnxùúCᦪᡠCᦪWûᐵoy=xḄWûnty=2-xḄWûüᐵoÈ=®ḄWûntᡠeA(A,,e")ö3(Ü,1Ḻ)ᐵoent&+஽=2,e*+ln%=2,ᦑAB;

16ᵫúCᦪḄឋ
X2=e",/(x)=e'+x—2ᓫ⌴=ᡠ஺,ᡠ/=᮱,ᦑC┯xᦪy=e”Ḅᦪ!",ᦪ)=2-xḄᦪ!g,#(|)=',ᡠ()ᡠ*Ḅ,(-)./ᓰ2+ὃ=252-m+422„,3᦮3,ᡠx5+ὃ3,ᦑD67.ᦑ⌱5ABD.23.(2022:;•=>?=>@ABC▤EFG)HI᜻ᦪ/(x)ᙠRL
MᐸMᦪf'(x),O஻1QR—f(l+x)+2x=0ឤᡂVW“X)ᙠ
0,1ᓫ⌴ᑣ()A.“X)ᙠ
1,2Lᓫ⌴YB.40)=0C./(2022)=2022D./'(2023)=1ூ[ᫀ௃BCDூ^᪆௃`aQ5bA,W/(x)=x,cᔠ⚪fᦑ┯gbB,HI᜻ᦪ“X)ᙠRL
Mᡠ/(0)=0,ᦑ67bChD,ig(x)=/(x)-X,ᑣg(x)RL
MḄ᜻ᦪ,gj=0,ᵫ⚪f/(l—x)+x—l=/(l+x)-1—x,g(l—x)=g(l+x),g(x)ᐵbmnx=lo᧕᜻ᦪg(x)ḄQqᕜs4,g(2022)=g(2)=g(0)=0,ᦑC67,ᵫoឋ
Ig(x)ᐵbmnx=-lou3
g'(-l)=0,(ᐸvwxyzᜓ|)Og'(x)ḄQqᕜs4,ᡠg'(2023)=g(—l)=0,ᦑD67.ᜓ|5g(l-x)=g(l+x),ᓽ-g(l-x)=—g(l+x),ᡠg(—l+x)=g(—l—x),~xMg'(-l+x)=-g'(-l-x),x=0,gீT)=Q᜛(-1),ᡠg'(-l)=0.`a5bA,W/(x)=x,cᔠ⚪fᦑ┯gbB,HI᜻ᦪ஻x)ᙠRL
Mᡠ/(஺)=0,ᦑ67bC,/஺QRQ/(1+R+2=0@Ḅᣚ+1,஻-x)-/(2+x)+2x+2=0,ᡠ/(x+2)+/(x)=2x+2,
/(x+4)+/(x+2)=2x+6,Y/(x+4)-/(x)=4,

17ᑣ“6)-"2)=4,/(10)-/(6)=4…/(2022)-/(2018)=4,(2022)-*2)=2020,ᵫ/(x+2)+஻x)=2x+2,஻2)=—/(0)+2=2,ᡠ/(2022)=/(2)+2020=2022,ᦑ67bD,/0_x)_/(l+x)+2x=OḄxMQ(1_)_/'(1+R+2=0,x=o,rপ=1-r(T)=஻x)ḄxM,஻QR=/ீᑗ,ᡠr(T)=I,஻x+4)-/(x)=4ḄXMr(x+4)=r(x),ᡠ/'(2023)=/'(2019)=…=r(-l)=1,ᦑ67.ᦑ⌱5BCD24.(2022ᓭ•Q@BC▤EFG)HIᦪ“Rg()ḄR,g'(x)g(x)ḄMᦪ,O஻x)+g'(x)T0=0/(x)-g((4-x)-10=0,Wg(x)Ꮤᦪᑣ¢ᑡQᡂVḄᨵ()A./প+"3)=20B.44)=10C./(-1)=/(-3)D./(2022)=10ூ[ᫀ௃ABDூ^᪆௃g(x)¥Ꮤᦪ,ᑣg(-x)=g(x),M-g'(-x)=g'(x),ᡠg'(x)¥᜻ᦪᦑg'(0)=0.ᵫ஻x)+g[x)-10=0,f(x)-¦(4-x)-10=0,/(x)—10=-g(x)=g(4-x),ᓽg'm+4),ᡠg'(x)¥ᕜsᦪOᕜs4,g'(0)=g'(4)=0,g'ফ=g'(2-4)=g'(-2)=-gঝ),ᡠg(2)=0.⌱⚗A5x=l/(l)+g,(l)->0=0,x=3,/(3)-^(1)-10=0ᦑ/(1)+/(3)=20,ᡠ⌱⚗A67.⌱⚗B5I,“4)-g'(O)—10=0,ᦑ"4)=10,ᡠB67.⌱⚗C5-1,/(-l)+g(-1)-10=0,*=-3,/(-3)-/(7)-10=0,ᓽW஻T)=/(-3),ᑣg'(T)=-g'(T),ᡠg'(-l)=0,¬g'(—l)Q0,C┯⌱⚗D57(2022)+^(2022)-10-0,ᵫg'(x)¥4ᕜs஻2022)+g'(2)—10=0,ᵫg'ফ=07(2022)=10,ᦑD67.ᦑ⌱5ABD.25.(2022ᓭ•®¯@ABC▤EFG)ᙠ6°☢²A8CO@WA8=&ᑣ¢ᑡ´a67Ḅ¥)

18A.µ°☢²᜜·ᳫḄ⊤☢º3»B.mnAB¼½☢88ᡠᡂ¾Ḅ6¿!V3C.᝞ÁÂA/ᙠ஺஺Lᑣ+ḄᨬÄ!ÅD.xnEABQqC~ᑖÂO¼ABᚖmḄ½☢ȵ°☢²ᡠÈ☢ḄᕜÉ2—+2Ê3ூ[ᫀ௃ACD6°☢²A8C஺@43=0Ë@Â஺᜜·ᳫḄᳫÌÍÎR=Q4=O8,஺|ÏBCDḄ᜜Ì,CÑ_V_⌭ᡠÐQ3■QÔ■,ᵫb0ᵪ2+005=°82,TᵫFBE=Ö,F,AOஹ=2×OAB¼½☢3c஺ᡠᡂḄ¾Ø4801,ᵫ“Ù=2=2*,ᦑ8Úg'ABH3AEJ_CDbE,ᡠAM3“=AE5BEC஺bE,ᡠ83“=3£“¼EÂÛᔠ40+BMᨬÄᨬÄ!2x᝞="ᦑC672ᙠ½☢ABC@xÂTÜPT_LABÝACbP,ᙠ½☢AQC@xÂ7ÜATJ_ÝADbR,Þ·R,RrcPTur,ᡠA8J_½☢77ß½☢7PRᓽᡠTP=TR=J^-,AD=PR=—,33ᑣÏ??/?ḄᕜÉá+O+á=m&â3333#ᳮᙠ½☢ABC@xÂNÜNQ_LA8Ý8CbQ,ᙠ½☢ä@xÂNÜNSJ_ABÝ80bS,

19Þ·QS,
½☢NQS,3½☢NQSᓽᡠNQ=NS=—,BQ=QS=AP=^!^,ᑣANQSḄᕜÉ᝞+⌭+á=2#+2è,ᦑD67.3333ᦑ⌱5ACD.26.(2022ᓭ•®¯@ABC▤EFG)Wðᙠñòᦪkh6,ôᦪ(x)hG(x)ᐸ÷ᐳLḄùfñᦪxúûü5ýþÿ+6G(x)M"+8ឤᡂᑣ)=+(x)G(x)Ḅ“◞”ᦪ஻x)=f(xeR),g(x)=g(x<0),஻(x)=2elnx(e-ᯠ/ᦪḄ0ᦪ)ᑣ()A.hHᑁᓫ5⌴7B.f(x)g(x)9:ᙠ“◞”,<=Ḅ>?AB[-M]C.f(x)g(x)G9:ᙠ“◞”<ுḄᨬJ?TD.“X)஻(x)G9:ᙠNOḄ“◞"y=2Q-eூSᫀ௃ADூV᪆௃AXY/n(x)=஻x)-g(x)=f—(,xe*4tn^x)=2x+Jு0,ᦑ^(x)ᙠᑁᓫ5⌴7,ᦑA_`;x2>kx+b/bB,CXcf(x),g(x)Ḅ◞de+fᑣ1/hix<0ឤᡂ,—0/hix<0ឤᡂkx2+bx-i<0ᵫkx2+ᮞO1W0/hix<0ឤᡂm᝕00o&=0,ᑣ=0qᔠ⚪io&<0,ᑣfOtO>o/hitwᡂxyy=f—"O஻Ḅ/zx=g2<஺|}4=+4஺஺,ᡠxy=Ax?+ᮞ-1Ḅ/zx=O340,A=h2+4k<0,Bpk2<-4b5.b2<-4k,2k4

20DXᦪ஻(x)Ḅᙠᡝᜐᨵᐳ,o:ᙠ(x)Ḅ◞,ᐳc◞Ḅ᳛ᑣ◞fy-e=Mx-A),ᓽy=fcc-%+e,ᵫ/(x)2"-&V^+e(x>0)ឤᡂo=0,ᑣf-eNO,(x>0)¡ឤᡂIk<0,ᵫx?-fcr+Z6OeN0(x>0)ឤᡂJu(x)=£-kx+kK-e,(x>0),ᑣ"(x)ᙠ(0,¢)ᓫ5⌴7”()=0,ᦑ&<0¡ឤᡂ¡qᔠ⚪iᦑ&>0,mf-£+%&-e±஺ᙠx>0¤ឤᡂM(X)=-Ax+ZXVe-eḄ/zx=*>0,ᑣ'=,-2¢¥M0¤¦ᨵ=26¤y=2§x-e,¨☢ª«/z(x)<27ex-e,YG(x)=2Gx-e-h(x),ᑣG[x)=2"[L),᧕m0¢¤G'(x)>0,ᦪᓫ5⌴7ᦑx=¢¤ᦪ>m᩽J?0,±BᨬJ?ᡠG(x)W0,ᦑ஻(x)42²-e,ᡠ<஺)(:ᙠNOḄ◞y=2&x-e,ᦑD_`.ᦑ⌱XAD.27.(2022•µᓭ·¸¹ºO»¼½¾▤ÀÁÂ)ᐵbᦪ஻x)=4cos2x+4sinxcos(x+£|,¨ᑡÅÆ_`ḄB()A.o¾Bᦪf(x)ḄÇᑣÈ-ᵯB1Ḅ᦮ᦪËB.ᦪf(x)Ḅᐵb/C.ᦪ஻x)ḄÌᦪy=26cos[2x-£)+lḄÍD.ᦪ/(Î)Ḅᵫy=24sin2xḄᐜᔣÑÒ1ᓫÓÔÕÖᔣ×ÑÒ?ᓫÓÔÕmᑮூSᫀ௃BCூV᪆௃/(x)=4cos2x+4sinxcos(x+?)=2+2cos2x+2>/3sinxcosx-2sin2x=1+3cos2x+V3sin2x=2\/3sinI2x+—\+],

21/(X)ḄÌXzÍÙḄÚÛḄÜ¡ÍÝ<¡ᦑA┯Þysin[2x(-£j+g=0,ᡠᦪy=2Gsin(2x+?)Ḅᐵb(-ãäåᑣᦪ஻x)Ḅᐵb,gl)/ᦑB_`Þᦪ/(x)=2Gsin(2x+2+l=26cos(2x-[+l,ᦑC_`Þᦪ/(x)Ḅᵫy=2&sin2xᐜᔣÑÒ1ᓫÓÖᔣ×ÑÒgᓫÓÔÕmᑮᦑD┯.6ᦑ⌱XBC28.(2022µᓭ·¸¹ºO»¼½¾▤ÀÁÂ)ᦪ/(x)§ᐸèᦪ/(éḄêëìᙳR,ᐵ'(0,0)
஻(x)@ABCᵫMMᢥᔣG(4,4)HIJK,ᦑC
5ᵫC⌱⚗;O%+*2=8R/?(^)+/1(%2)=8,ᵫUᦪᑡឋW4+4=8,.1஻(aJ+Mᓽ)=8,A\]^᎔`aDcd.ᦑ⌱eBCD

22/ஹ2r-2,x329.(2022gᓅijklmnopqr⚜t)u;ᦪ஻v)=τ,1Mwᦪ-X2+8X-12,X
3g(x)=[f(x)]2-(2t+[)f(x)+t2+t,ᑣyᑡz{cdḄ()A.|g(x)ᨵ4~ᑣ344B.ᙠᦪr,Kg(x)ᨵ5~C.Og(x)ᨵ6~R.ᑖ,஽,,,,஽yᓃ3%,ᑣ2X'+2X-+2x,+2Xi=8D.
r0,g(x)ឤᨵ2~ூᫀ௃BCூ᪆௃/5)Ḅᜧ=>᝞=ᡠx)=0,ᓽ"(X)T]"(X)T—1]=0,ᓽf(x)=rᡈ/U)=r+1.|g(x)ᨵ4~ᑣᦪrḄ¡£344ᡈf=2ᡈnᦑA⚗┯¤5ᵫ=@;O1=1Rg(x)ᨵ5~ᦑB⚗cd5Og(x)ᨵ6~Rᑣ᳝¦21§ᓃ2,ᡠA(2-2Xl=2Xj-2¨,ᓽᨵ2%+2*+2++2$=8ᦑC⚗cd5ORg(x)ᨵ4~ᦑD⚗┯[2-29=2X,-2¤ᦑ⌱eBC.30.(2022.gᓅ.©lopª▤¬®)u;ᦪᑡ4,஻¯ᙳ⌴²ᦪᑡ³´Ḅµ஻⚗!ᑖS“T„,¶·%+஺ᔣ=2"஻¹ಘ=2",ᑣyᑡ»¼cdḄ()A.0«,1B.S=n2+3n-2C.1½0D.5,„T2n2nூᫀ௃ACD¾+W=2ூ᪆௃ᵫÀ஻,,¯⌴²ᦪᑡK4Ḅ/5Na“+aO=2஻MᡠAfn.q+%>2a,ᡠA,ᡠAᦑ⌱⚗Acd;a+a>2a=4-4a,232

23•*-S2n=(q+஻2)+(஺3+஺4)-Ã(஺2஻1]+ain)=2+6+10d---F2(2/2—1)=2஻",ᦑBcd;ɹ=2ᵫÀʯ⌴²ᦪᑡab2Vb3,QbR2=2஻,ᡠA];.ெ᝛=4ᡠAÍᡠA1஽⊈ᦑ⌱⚗ccd5ᡠAÐ=(A+4+…+4”|)+(4+¾+,,,+%)*(1-2")+"(1-2")=(4+Ô(2"-1),ᡠA&22M(2"-1)=20(2"-1),Qb#S,ᡠAÖ>20(2"—1),J20(2"-1)-2/=2(72-2"-n2-⊈)O”Ù5Rஹ2(V2-2"-n2->/2)>0;O1<஻44R@Þß2(a-2"-"2nà>o,ᡠA
'Ḅ“eN“5„<75„,ᦑ⌱⚗Dcd.2ᦑ⌱eACD.31.(2022gᓅ•©lopª▤¬®)u;஺ᙶ᪗éᙊC:(x-cose)2+(y_sin6)2=I,ᑣyᑡ»¼cdḄ()A.ᙊ஺ឤñé஺B.ᙊ஺Öᙊf+y2=4ᑁᑗC.ó%x+y=ôõᙊ஺ᡠöK÷øḄᨬᜧ¡úD.ó%xcosa+ysina=஺Öᙊ஺ûூᫀ௃ABCூ᪆௃A.üᐭ(0,0)K(-cos6)2+(-sine)2=1ឤᡂÿABVcos20+sin2^=|l-2|.ᓽᙊᙊBC.%&x+y=¥*ᙊCᡠ,-./0sin6+cos8#sin6+cos஺#sin0+cos0=Tsin10+?22

24ᓽ%&x+y=*ᙊ஺ᡠ,-./Ḅᨬᜧ706,CD.ᙊᑮ%&Ḅ;c*+smma|=cos(®_a)G,ᦑᙊE%&FᑗᡈFID┯KVcos2cr+sin-aᦑ⌱NABC.32.(2022PQRᜧT▬VWX▤Z[\)]ᦪ/(x)=J5sin3x+9)(3>0,5<ஹ)Ḅfᑖhi᝞hᡠk,ᑣmᑡopVḄᨵ()A./(x)ḄᨬrᕜtT0v3vB./(x)ᔣxyz9{ᓫ}~-ᑮḄ]ᦪᏔ]ᦪOC./(=1ᙠ(0,ভᐳᨵ4{᪷ᑣ4{᪷ḄE0D./(x)^xe0,,])hiḄMᑮ%&2x-y+4=0ḄᨬrMḄᙶ᪗0?.ூᫀ௃ACDூ᪆௃0஻x)¡(¢0)ᡠ£/(¤¥¦§(+᜛)=0,©ªᙠf(x)Ḅᓫ¬⌴®¯°ᑁᡠ£#^ߟ+஺=»+2ᓃeZ)জ8©0·¸¡¹º)ᡠ£/¹¥&sin(¼+9)=1,Sin(+9)=#©x¿/(x)=lᙠᨬrḄᡠ£+᜛=¿+2ÀÁᓄeZ)ঝ.ὶÅজঝÆ-=T-0=2,ÇᐭজÆ-e=-?+2᱐•,(4€Z),©ᑬ<],ᡠ£᜛=-7,ᑣ/(x)=&sin(2x-?).ᦑf(x)ḄᨬrᕜtT=/=vᑣA“X)ᔣxyz᧖{ᓫ}~-ᑮḄ]ᦪg(x)=V5sin21-Ò_N=ÓÔ(2Õ-Ö)=>/2sin(2x-=-72sin2xᑣg(x)0᜻]ᦪᦑB┯KØ/(x)=lᙠ(0,পḄ4{᪷ÚᜧᑮrÛÜ00‘Þß“J2x/=gᑣx=3,᪷à“X)Ḅáâ

25ឋÆ-Xä=9ᑣᵫ/(X)ḄᕜtឋÆ-᳝ç1=è+7=¥ᡠ£éê=2ë+ì)=?2o2oo,=í\®o/ZᦑCNïß%&/N2x-y+4=oyðḄ%&ñᐸß/(X),¥€0,ßí)ᨵóᐳᑣᙠôḄ¡VõᨵÞ%&ß0,öí)Fᑗ%&/'ß%&/øᙠᨬrùMᑮ%&2x-y+4=஺ḄᨬrU,ú:(ü=2ýcos(2x-(1=2,ᑣ2x-?=±?+2brQeZ),x=br,(ZeZ)ᡈx=?+᱐,(ZwZ),xe0,^,ᡠoᡈ(ᡈ()஻0)=-1,!(O,T),=$2(£,11,ᑣᵫ|1+4|+"4,-.ᑮ01/Ḅ45ᜧ7ᑮ01/Ḅ45ᡠMᑮ012x-y+4=0Ḅ45ᨬ;<MḄ=ᙶ᪗@AᦑDDE.4ᦑ⌱HACD.33.(2022LMNᜧP▬RST▤VWX)YZ[P(l,2)ᨬ^-_`஻(஻eN*)ᩩ01deᦪf(x)=(x-l)e”Ḅijkᑗ,ᑣ()A."-mn"3B.7+஻<4C.r᮱1<4Ḅmtuv18,-£|D.r஻=2<xᙠz+Ḅ;Itூ~ᫀ௃ABDூ᪆௃y'=e+(x-l)e=xe*ᑗ1/Ḅᑗ[@(%,%),ᑣᑗ1/Ḅ᳛@=%e%,%=(x()T)e□,ᑣᑗ1/Ḅ@y-(x<)T)e&=xe'l)(x-x),oo.../e%=5-1)+'=e"--ᑣ2=-e-U-l)2,0஽-1J^-1g(x)=-e(x—,ᑣgl<g'(x)<0,r<g'(x)>0,ᡠeᦪg(x)ᙠ(f,T)(l,+8)ᓫ⌴ᙠᓫ⌴g(-l)=-±gপ=0,rXf-00<g(x)-0.,rx->+oo<g(x)f-8,e_`eᦪg(x)Ḅ₝i᝞7A,ᵫ74=-e*(x0-l)2,ex«>O,(x-l)2>0,oᦑ/IWO,

26ᵫij-$஻=1ᡈ2ᡈ3,ᓽ஻¢3,ᦑADE£7B,¤@2=0d஻=3¥¦§

27q17C,¤@“X)ᙠ(1,2)ᓫ⌴ᡠf'(x)40,ᓽ/'(6=3/—2or—240,ᙠ(1,2)3131ឤᡂÍg(x)==x-±(xe(l,2)),ᑣg'(x)==+3>0,ᡠg(x)ᙠ(1,2)ᓫ⌴ᡠ2x2X"g(l)^-ax2-2xᙠxe[l,2]ឤᡂÍ,ᓽa"-lnx-2ᙠxe[l,2]ឤᡂÍ/z(x)=x-lnx-2,xe[l,2],ᑣ஻(x)=]¯+´=X++>0,XXXX'Xᡠ/z(x)xe[l,2]ᓫ⌴ᡠ஻(x)M=஻(2)=2-ln2-l=l-ln2,ᡠ/lTn2,ᡠD┯±ᦑ⌱HABCTஹêë⚪2235.(2023íMíî¹ïLSðRPST▤VWX)ñ$òᙊ*•+᧡•=Ù஻>ᓃ>0)Ḅᯖ[ᑖø@M(-C,O),6(c,0)(c>0),²ᩩúû14Hy=x-c,2Hy=x+cüòᙊ7A,B,C,஺ý[YA,B,C,஺@⚔[Ḅýÿ☢2஻ᑣᙊḄ᳛.ூᫀ௃2-72ூ᪆௃C(X],%),£>(4,%),y=x-cὶ$%&4'ᙊḄ()*X2V2bv=1᦮ᳮ23:᦮+b1)x2-2a2ex+a2c2-a2b2=0,2a2ccrc2-erb2…=Nᡠ:;|=HFJa+X2)2-4g〈C-4?EF+F)=G/W%&4,2IḄJdᡠ:LMNOḄ☢S=|8M="|TU2V7=W᦮ᳮ23*/+2X࠷-2/=0,ᓽ/+2[-2=0,3*e=—A/2+2,ᵫᙊḄឋ^23᳛e=2-`ᦑᫀ*2-X.,ஹf2|log,x|,xe(0,2136.(2022ij•lᵪ᜜opqrqs▤uvw)xyzᦪ=|I2+“)’()஻=ᨵNḄ᪷4ᓃᱏḄ.

28ூᫀ௃10,12ூ᪆௃zᦪḄ'ᓃ᝞.()/x=ᨵNḄ᪷ᑣ02ᡠ:¡“=2110g2Rᙠxe0,2]¤'¥=Ḅ¦§¨Ḅ©ᙶ᪗.ᵫ/5=/%ᓽ|log2%|Tlog2W|ᡠ:log?%+log2X2=0,ᓽlog2a=0,ᡠ:ᓰ஽=1±/x=xJ7x+12ᙠX«2,+8¤'y=mḄ¦§¨Ḅ©ᙶ᪗.ᡠ:+ᓃ=7µ/*=*2·7%+12=2¸Ḅ¦ᦪ᪷2,5,ᑣ2±3ᑣ“¹'ᑁ==s7-s=-k+7%,=-¼·1]+?,½2¾33ᡠ:-k+7seio,i2ᦑᫀ*10,1237.2022ij•lᵪ᜜opqrqs▤uvwÀ(ABCQOÄ1,¨Åᙠ&uAC¤ÆÇᑣÈ•É+(Ḅ.ூ᪆௃:A8,ACx,yÊË$%Ìᙶ᪗Íᑣ,

29A(0,0),8(1,0),C(l,l),Î(0,1),P(xಘ(OWxWl),ᑣAP=(x,x),PB=(1-x,-x),PD=(-x,l-x),.\AP^PB+PD^=2x(1-2x)=-4(x-F)+F(0Kxீl),µx¸zᦪᨵᨬᜧ!44µx=l¸zᦪᨵᨬ-2,.•.É.(É+È)Ḅ-2஺._4_ᦑᫀ*-2,).438.2022•ijÕÖ×ÕÖrØqs▤uvwxyzᦪ/Ù=31ᡃ¹Ù=ஹ%&¥=
0'zᦪ஻x,gxḄÛÜÝᑗᑣ+gḄᨬ__________.bூᫀ௃4eூ᪆௃᪷à⚪â₝᝞ä:

30

31P(x,y),ᑣF(1,0)ᐵçP(x,y)èéḄ¨Ḅᙶ᪗(2x-l,2y),2(2x-1+1ê+(2yp=16,ᓄí3¨ÅḄîï()x?+)/=4,ᓽ¨ÅḄîï:ð¨ᙊ:2ñòḄᙊὡ(TO),ᡠ:õὡḄᨬᜧ3.ᦑᫀ*340.(2022•öᓭᴉù·rqs▤uvw)xyzᦪ/(x)=e',g(x)=lnT+g,èüâmeR,ýᙠ«6(0,-K»)
f(m)=g(")ᔓn-mḄᨬ.ூᫀ௃3+ln3ூ᪆௃=1஺0)ᑣ=lntn|1ᵫ⚪$In&+&=

ᡠ(3)§33஻,De(=3e3-Inz\τ11Cx)=3e%(x)=3e)-,t᧕$஻'(x)=3e'T_1ᙠ(0,+8)<ᓫ>⌴@,ABᑮ஻(D)=0E
F0,D),//(஺<0,I)ᓫ>⌴JEK>0,6Kᓫ>⌴@ᡠ(஻KḄᨬ1(£|=3-lng=3+ln3ᡠ(“,PḄᨬ3+ln3ᦑᫀR3+ln341.(2022UᓭWXYZ[\▤^_`)a$bᦪ/")=d
g(x)=2e
fbᦪ2xx-m/7(x)=g(f(x))+ᨵ3jklḄmnxl,x2,x3(xl

32,“X)=Ḅbᦪr(x)="y)(x>0),sr(x)<0,zx>e,r(x)>0,z0-oo;x-^-H»,/(x)-»0f(l)=0D⌕bᦪ/7(x)=g(/(x))+Pᨵ3jklḄmn
(1)f(x)=£,ᨵxjklḄ
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-
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33¨0,ᦑ8(x)@bᦪ
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fÞᙠßjklḄnPáâ54248
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34ூᫀ௃|ூ᪆௃ᵫÚÿឋ
PᙠXᓃP(c,஻?),஻z>0,APOF=a,4PAF=BmmtanZ.APO=tan(a-/?)=ca+cam_aa0'2g(x)=/(x)+4(x)+lាlᨵnop*ᑣrᦪ4Ḅ!HstூKᫀ௃r-22'+U<0ூw᪆௃yz_ᦪ஻x)=|2}X>஺Ḅ᝞,

35

36ᡠ<=-2a2-4x3aV0,w04a43,a=0,/஺=ᙠ—,0(ᓫ⌴0W3,ḄIᔣ(Ḅᱥ'ᡠ0,/=4-/*"Iᓫ⌴_ᦪ,4-a2>04-a2<0ᡠ0ᡈ0(4-a2)e°>0-22ᡈ஺<-2ᡠ\ᡈ

37ঝ·Iv-bMOᓽ04ᓃ<1_ᦪg¯ᙠ¼-L4)(ᓫ⌴½ᙠ(TM¿(ᓫ⌴,ᦑg(f)min=g(Ã:·?ஹ.¤g(f)mx=max{g(_l),g(l)}=max{g_ᓃ+c-¤¤++c_(}=¤+6+c-¤,³IJᨵ+b+C——-+Ê஻+2ᓃ·740w·1-20W8W-1+2ᦈµO<1¤ঞᓽ·1<6<0_ᦪg¯ᙠ(ᓫ⌴½,ᙠ(RJᓃᓫ⌴ᦑg(%n=g(-6)=-?2+C-¤³IJᨵg")max_gWmin=(¤_A+C_¤)_(_;b?+C_¤)=¤/·6+¤44,ÊÓ-28-740w1-2⊈4641+2Õµ·1<6<0Mট-621ᓽbV-l_ᦪg(஺ᙠ¼T1¿(ᓫ⌴½³Ug")max_g(r)min=g(T)_g(l)=(g_6+C_¤)_(¤+Z?+C_¤)=_2644,wZ?N—2,µ--2<&<-l.Ù(ᡠÚrᦪ6Ḅ!Hst¼-2,2¿.QᦑKᫀIM(1)(2)¼-2,2¿.48.(2022Üᓅ•Þßàá·VTâã⚜å)⁐çᳮéê⁐ëìஹ⁐⚪tíîïðXᜧᦪTñ⚪ò·.ᙢ⁐çᳮᨬᐜtᵫ·ö÷øùúḄûüᜧTýþzᩭḄ.⁐ᳮḄᑁ“ᙢᵨ⁐ᐹᨵᐳḄ!"Ḅ⁐#$ᙠ&'(!Ẇ*+,-ஹ/ஹ0ஹ14⁐3⚪5᝞5719ᨵ1:';5729ᨵ2:';5…57஻9ᨵ஻:';5?4⁐ᙠ@9AᑖCD9,⁐5@9EFḄ';⁐"5G4H7k9",⁐ᦪ5ᑣ%=,*=1

38”:';ூRᫀ௃324(2஻-1)3"+1ூ[᪆௃ᵫᑖ^_ᦪ`ᳮa@9Ḅ7:';ᨵ4b,c5ᐸe@:';ᙳᨵ3,c5ᦑ4=4x3,=3245a“=4x3"-’,ᑣS“=£kq=4(lx30+2x3'+3x32+---+n-3n_1)®,k=lᡠu3s“=40x31+2x3?+3x3,+…+”-3")ঝ5জ-ঝz-2S“=4(30+31+32+…+3"T_஻.3")=-3j=(2-4஻)3"-2,ᓽS,=(2஻-1)3"+1.ᦑRᫀH324,(2஻-1)3"+149.(2022ᓅA$▤)ᙠA8C஺A5AB=6,BC=1,?ABCACᢚ5zᑮ☢D48C,ᑣ☢᜜ᳫḄ¡H¢£¤☢஺AC—8Ḅ¦☢H஺5§7T7T஺ᙠ¨55ᑁªᓄ¬58஺Ḅ®°H.ூRᫀ௃±²³ூ[᪆௃᝞1,ᑖC´µB,஺¶8·5AC,DE1AC,ᚖ¹ᑖCHºE,ᑣᙠ☢ABC£>A¼½¹3AC,DEIAC.¾H=BC=\,ᡠuAC=2,DE=BF=^^-=—,22ᑣAE=CF=g,EF=1.12ᙠ☢A8C஺A5A8CÂZMCᙳHÅ5£µ஺HACḄAµ5᝞2,Æ஺8,OD,ᑣAO=OC=OB=OE>=1,

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