1.函數(shù)f(x)滿足f(x+2)=f(x),當(dāng)-1≦x<1時(shí),f(x)=x^2+1,則當(dāng)x∈[2n-1,2n+1)且n∈Z時(shí),f(x)=___2.函數(shù)f(x)的圖象關(guān)于直線x=1對(duì)稱,當(dāng)x≦1時(shí),f(x)=x^2+1,則當(dāng)x≧1時(shí),f(x)=___答案是1.(x-2n)^2+1 2. (2-x)^2+1
熱心網(wǎng)友
1,由f(x+2)=f(x)可知其周期為2, 設(shè)2n-11時(shí),y=f(x)上任一點(diǎn)(x,y),關(guān)于x=1的對(duì)稱點(diǎn)為(x1,y1),則由對(duì)稱可知x1+x=2,y=y1,x1=2-x,y1=y,因?yàn)?x1,y1)在當(dāng)x≦1時(shí),f(x)=x^2+1上,所以有y1=x1^2+1,代入得y=(2-x)^2+1