奇函数f（X）的定义域为R，f（X 2）为偶函数的意思 奇函数f(x)的定义域为R,若f(x 2)为偶函数,且f(1...
\u5947\u51fd\u6570f\uff08x\uff09\u7684\u5b9a\u4e49\u57df\u4e3aR\uff0c\u82e5f\uff08x+2\uff09\u4e3a\u5076\u51fd\u6570\uff0c\u5219f\uff088\uff09\u5947\u51fd\u6570f\uff08x\uff09\u7684\u5b9a\u4e49\u57df\u4e3aR\uff0c\u6240\u4ee5f(0)=0\uff1b
f\uff08x+2\uff09\u4e3a\u5076\u51fd\u6570\uff0c\u6240\u4ee5f(x+2)=f(-x+2).
\u6240\u4ee5f(8)=f(6+2)=f(-6+2)=f(-4)
\u800cf(-4)=f(4)\uff0c\u6240\u4ee5f(8)=f(4).
\u7531\u4e8ef(4)=f(2+2)=f(-2+2)=f(0)=0
\u6240\u4ee5f(8)=0
f(x) \u662f\u5947\u51fd\u6570\uff0c\u5219 f(-x)\uff1d - f(x)\uff0c
f(x\uff0b2) \u4e3a\u5076\u51fd\u6570\uff0c\u5219 f(-x\uff0b2)\uff1df(x\uff0b2)\uff0c
\u6240\u4ee5 f(x\uff0b4)\uff1df[(x\uff0b2)\uff0b2]
\uff1df[-(x\uff0b2)\uff0b2]\uff1df(-x)\uff1d - f(x)\uff0c
\u6240\u4ee5 f(8)\uff1df(4\uff0b4)\uff1d- f(4)\uff1df(0)\uff1d0\uff0c
f(-7)\uff1d- f(7)\uff1df(3)\uff1d- f(-1)\uff1df(1)\uff1d1\u3002
绛旓細銆
绛旓細f (X +2)鏄伓鍑芥暟璇存槑f (X )鍏充簬x =锛2瀵圭О
绛旓細瑙ｆ瀽锛氬洜涓篺锛坸锛夊湪R涓婃槸濂囧嚱鏁颁笖f锛坸+2锛変负鍋跺嚱鏁 锛屾墍浠(x+2)=f(-x+2),f(x+2)=-f(-x-2),鐢辨鍙煡f(8)=f(-8+2锛=f锛6锛=f(4)=f(0)锛屽洜涓哄鍑芥暟f锛坸锛夊畾涔夊煙涓篟,鎵浠锛0锛=0锛屾墍浠锛8锛=f锛0锛=0锛屽洜涓篺锛1锛=1锛屽悓鐞嗗彲璇乫锛9锛=f锛7锛=f锛5锛=f锛...
绛旓細濂囧嚱鏁癴(x)鐨勫畾涔夊煙涓篟,鍒檉(0)=0 xf(x)<=0 (1)x<=0,f(x)>0 -lg(-x)>0,lg(-x)<0,0<-x<1,鍗-1<x<0 鎵浠ユ湁:-1<x<0.(2)x>=0,f(x)<0 lgx<0,0<x<1 鎵浠,0<x<1.缁间笂鎵杩,瑙ｉ泦鏄(-1,0)U(0,1)
绛旓細鍗砯(-x+2)=f(x+2)鍗砯(-锛坸+2锛+2)=f(x+2+2)鍗砯(-x)=f(x+4)鍗砯(x+4)=f(-x)=-f(x)鍗砯(8)=f(4+4)=-f(4)=-f(0+4)=-[-f(0)]=f(0)=0...(娉ㄦ剰f(x)鏄濂囧嚱鏁帮紝鏁協(0)=0)f(9)=f(5+4)=-f(5)=-f(1+4)=-[-f(1)]=f(1)=1 鏁 f(8)+f...
绛旓細濂囧嚱鏁癴(x)鐨勫畾涔夊煙涓篟,鏁呮湁f(x)=-f(-x),鈭磃(0)=0 璁緓0 鈭靛綋x锛0鏃,f(x)=2x²+x 鈭-x>0,鈭磃(x)=-f(-x)=-[2(-x)²-x]=-2x²+x {2x²+x,x>0 鈭磃(x)={0,x=0 {-2x²+x,x ...
绛旓細f(x)鏄懆鏈熶负2鐨鍑芥暟锛屾墍浠ワ細f(x)=f(x+2)锛3/2<=x+2<=2 鎵浠ワ細f(x+2)=x+x^2=(x+2)^2-3(x+2)+2 鎵浠ワ細褰3/2<=x<=2鏃锛宖(x)=x^2-3x+2 褰0<=x<=1/2鏃讹紝f(x)=x-x^2锛岀敱锛1锛夌煡f(1+x)=-f(x)=-x+x^2=(x+1)^2-3(x+1)+2锛1<=x+1<=3/2...
绛旓細f(x) 鏄濂囧嚱鏁锛屽垯 f(-x)锛 - f(x)锛宖(x锛2) 涓哄伓鍑芥暟锛屽垯 f(-x锛2)锛漟(x锛2)锛屾墍浠 f(x锛4)锛漟[(x锛2)锛2]锛漟[-(x锛2)锛2]锛漟(-x)锛 - f(x)锛屾墍浠 f(8)锛漟(4锛4)锛- f(4)锛漟(0)锛0锛宖(-7)锛- f(7)锛漟(3)锛- f(-1)锛漟(1)锛1銆
绛旓細=-f锛1-锛坸+1锛夛級=-f锛-x锛=f锛坸锛夛紝鎵浠锛坸锛夋槸鍛ㄦ湡涓2鐨鍑芥暟锛庯紙2锛夆埖褰搙鈭圼12锛1]鏃锛宖锛坸锛=f锛1-x锛=锛1-x锛-锛1-x锛2=x-x2锛屸埓x鈭圼0锛1]鏃讹紝f锛坸锛=x-x2鈭村綋x鈭圼1锛2]鏃讹紝f锛坸锛=f锛坸-2锛=-f锛2-x锛=锛2-x锛2-锛2-x锛=x2-3x+2锛庘埓褰搙鈭...
绛旓細绛変簬1 銆傚垎鏋愬涓嬶細鍥犱负fx濂囧嚱鏁鎵浠0=0 銆俧x+2涓哄伓鍑芥暟锛屾墍浠 fx+8=-fx-8(鍥犱负濂囧嚱鏁)=-fx+4(鍥犱负fx+2鍋跺嚱鏁)=fx-4(濂囧嚱鏁)=fx(fx+2鍋鍑芥暟)锛鎵浠x鏄懆鏈熶负8鐨勫懆鏈熷嚱鏁般傛墍浠 f8+f9=f(8-8)+f(9-8)=f0+f1=0+1=1 ...
