f(x)是周期为2的奇函数,当X属于(0,1)时,F(X)=LOG2X,F(X)在（1，2）上解析式
\u8bbef\uff08x\uff09\u662fR\u4e0a\u4ee52\u4e3a\u5468\u671f\u7684\u5947\u51fd\u6570\uff0c\u5df2\u77e5\u5f53x\u2208\uff080\uff0c1\uff09\u65f6\uff0cf\uff08x\uff09=log2x\uff0c\u90a3\u4e48f\uff08x\uff09\u5728\uff081\uff0c2\uff09\u4e0a\u7684\u89e3\u6790\u5f0f\u8bbex\u2208\uff081\uff0c2\uff09\uff0c\u5219-1\uff1cx-2\uff1c0\uff0c\u22340\uff1c2-x\uff1c1\uff0c\u2235\u5f53x\u2208\uff080\uff0c1\uff09\u65f6\uff0cf\uff08x\uff09=log2x\uff0c\u2234f\uff082-x\uff09=log2\uff082-x\uff09\uff0c\u2235f\uff08x\uff09\u662fR\u4e0a\u4ee52\u4e3a\u5468\u671f\u7684\u5947\u51fd\u6570\uff0c\u2234f\uff08x-2\uff09=-f\uff082-x\uff09=-log2\uff082-x\uff09\uff0cf\uff08x\uff09=f\uff08x-2\uff09=-log2\uff082-x\uff09\uff0c\u2234f\uff08x\uff09=-log2\uff082-x\uff09\uff0c\u6545\u7b54\u6848\u4e3a\uff1a-log2\uff082-x\uff09\uff0e
\u89e3\u7531\u5f53x\u5c5e\u4e8e(0,2]\u65f6,f(x)=2^x-1,
\u77e5f(x)\u5728x\u5c5e\u4e8e(0,2]\u662f\u589e\u51fd\u6570\uff0c
\u6b64\u65f6\u51fd\u6570\u7684\u503c\u57df\u4e3a[0,3]
\u53c8\u7531f(x)\u662f\u5b9a\u4e49\u5728[2,2]\u4e0a\u7684\u5947\u51fd\u6570
\u6545f(x)\u662f\u5b9a\u4e49\u5728[2,2]\u4e0a\u7684\u503c\u57df\u4e3a[-3,3]
\u5bf9\u4efb\u610fx1\u5c5e\u4e8e[-2.2],\u5b58\u5728x2\u5c5e\u4e8e[-2\uff0c2]\u4f7f\u5f97g\uff08x2\uff09=f\uff08x1\uff09
\u77e5f(x1)\u5c5e\u4e8e[-3,3]
\u6545g(x2)\u5c5e\u4e8e[-3,3]
\u53c8\u7531
g(x)=x^2-2x+m
=(x-1)^2+m-1 x\u5c5e\u4e8e[-3,3]
\u5f53x=1\u65f6\uff0cg(x)\u6709\u6700\u5c0f\u503c\u4e3am-1
\u5f53x=-3\u65f6\uff0cg(x)\u6709\u6700\u5927\u503c15+m\uff0c
\u6545g(x)\u7684\u503c\u57df\u4e3a[m-1\uff0c15+m]
\u6545m-1\u2264-3\u4e1415+m\u22653
\u5373m\u2264-2\u4e14m\u2265-12
\u5373-12\u2264m\u2264-2\u3002
0<-x<1
所以f(-x(适用f(x)=log2(x)
则f(-x)=log2(-x)
奇函数f(x)=-f(-x)
所以-1<x<0
f(x)=-log2(-x)
T=2
则f(x+2)=f(x)
1<x<2
则-1<x-2<0
所以f(x-2)=-log2(-x)
则f(x)=-log2(-x-2)
绛旓細A 璇曢鍒嗘瀽锛 f ( x )鏄懆鏈熶负2鐨勫鍑芥暟锛f(x)=f(x+2),褰0鈮 x 鈮1鏃讹紝 f ( x )锛2 x (1锛 x ),閭ｄ箞鍙煡 f (锛 )锛- f ( )锛-f(2+ )锛-f( )=-2 鏁呯瓟妗堜负A.鐐硅瘎锛氫富瑕佹槸鑰冩煡浜嗘娊璞″嚱鏁扮殑濂囧伓鎬у拰瑙ｆ瀽寮忕殑杩愮敤锛屽睘浜庡熀纭棰樸
绛旓細濂囧嚱鏁f(x)=-f(-x)鎵浠-1<x<0 f(x)=-log2(-x)T=2 鍒檉(x+2)=f(x)1<x<2 鍒-1<x-2<0 鎵浠(x-2)=-log2(-x)鍒檉(x)=-log2(-x-2)
绛旓細A 璇曢鍒嗘瀽锛氳В锛氣埖f锛坸锛夋槸鍛ㄦ湡涓2鐨勫鍑芥暟锛屽綋0鈮鈮1鏃讹紝f锛坸锛=2x锛1-x锛夛紝鈭存牴鎹懆鏈熸у彲鐭ワ紝 f (锛 )锛 f (锛 )锛屽啀鍒╃敤濂囧嚱鏁版ц川鍙煡 f (锛 )=-f( )=锛 锛屾晠绛旀涓猴細A锛庣偣璇勶細鏈鑰冩煡鍑芥暟鐨勫懆鏈熸у拰濂囧伓鎬х殑搴旂敤锛屼互鍙婃眰鍑芥暟鐨勫硷紟
绛旓細瑙ｆ瀽锛氣埖鍑芥暟f(X)鏄懆鏈熶负2鐨勫鍑芥暟, 鈭村嚱鏁癴(X)鍏充簬鍘熺偣瀵圭О 鈭靛綋X鈭圼0,1]鏃讹紝f(X)=2X-2X^2锛屸埓褰揦鈭圼-1,0]鏃讹紝f(X)=-2^(-X)鈭祃og(1/2,23)鈮-4.5236 褰揦鈭圼-5,-4]鏃讹紝f(X)=-2^(-(X+4))鈭磃(log(1/2,23))=-2^(-(X+4))=-2^(0.5236)鈮-1.4375 ...
绛旓細1-X),姹俧锛堣礋鐨勪簩鍒嗕箣浜旓級瑙ｆ瀽锛氣埖鍑芥暟f(X)鏄懆鏈熶负2鐨勫鍑芥暟,鈭村嚱鏁癴(X)鍏充簬鍘熺偣瀵圭О 鈭靛綋X鈭圼0,1]鏃讹紝f(X)=2X-2X^2锛屸埓褰揦鈭圼-1,0]鏃讹紝f(X)=2X+2X^2 褰揦鈭圼-3,-2]鏃讹紝f(X)=2(X+2)+2(X+2)^2 鈭磃(-5/2)= 2(-5/2+2)+2(-5/2+2)^2=-1/2 ...
绛旓細鈭f锛坸锛夋槸鍛ㄦ湡涓2鐨勫鍑芥暟锛屽綋0鈮鈮1鏃讹紝f锛坸锛=2x锛1-x锛夛紝鈭磃(?52)=f锛-12 锛=-f锛12锛=-2脳12 锛1-12 锛=-12锛屾晠绛旀涓猴細-12锛
绛旓細A f =f =f =-f =-2脳 脳 =- .鏁呴堿.
绛旓細f(x)=(0.5)^(x-4)鍏堝埄鐢鍛ㄦ湡鎬у钩绉诲埌鍖洪棿锛-1锛0锛夛紝鍐嶅埄鐢ㄥ鍋舵у彉鎹
绛旓細log1/3(23)= -lg3(23 )lg3(9)=2<lg3(23) <log3(27)=3 -3<-lg3(23 )<-2 褰搙鈭(0,1)鏃,f(x)=2^x 濂囧嚱鏁,f(-x)=-f(x)鎵浠 x鈭(-1,0),f(x)=-2^(-x)鍛ㄦ湡涓2, x鈭(-3,-2,),f(x)=-2^(-x)鎵浠ュ師寮=-2^(-log1/3(23)) =-2^(log3(23))...
绛旓細a=f(6/5)=f(6/5-2)=f(-4/5)=-f(4/5)=-lg(4/5)b=f(3/2)=f(3/2-2)=f(-1/2)=-f(1/2)=-lg(1/2)c=f(5/2)=f(5/2-2)=f(1/2)=lg(1/2)0锛x锛1鏃讹紝lgx<0锛屾墍浠<0锛岃宎銆乥>0锛屾墍浠<a
