函数y=(2x^2-x+1)/(x-1),x∈(1,+∞)的值域是多少?

题目

函数y=(2x^2-x+1)/(x-1),x∈(1,+∞)的值域是多少?

答案

y=[(x-1)(2x+1)+2]/(x-1)
=(x-1)(2x+1)/(x-1)+2/(x-1)
=2x+1+2/(x-1)
=2(x-1)+2/(x-1)+3
x>1,x-1>0
所以2(x-1)+2/(x-1)+3≥2√[2(x-1)*2/(x-1)]+3=4+3=7
所以值域[7,+∞)