问题描述: y=(x²+2x+3)/(x²+1)的值域, 1个回答 分类:数学 2014-12-12 问题解答: 我来补答 y=(x²+2x+3)/(x²+1)=1+2(x+1)/(x²+1)求导可得y'=-2(x²+2x-1)/(x²+1)²令y'=0可得x=√2-1或-√2-1lim(x→∞)(x²+2x+3)/(x²+1)=1当x=√2-1时y=(3√2+6)/4取得最大值当x=-√2-1时y=(6-3√2)/4取得最小值∴y=(x²+2x+3)/(x²+1)的值域为[(6-3√2)/4,(3√2+6)/4] 展开全文阅读