求函数y=(x^2+1)/(x-1)(2

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求函数y=(x^2+1)/(x-1)(2求函数y=(x^2+1)/(x-1)(2求函数y=(x^2+1)/(x-1)(2令t=x-1==>1≤t≤2x=t+1x^2=t^2+2t+1y=(t^2+2t

求函数y=(x^2+1)/(x-1)(2
求函数y=(x^2+1)/(x-1)(2

求函数y=(x^2+1)/(x-1)(2
令t=x-1 ==> 1≤t≤2
x=t+1
x^2=t^2+2t+1
y=(t^2+2t+1)/t
=t+(1/t)+2
函数y=t+(1/t)+2在[1,2]上是增函数,所以
y(max)=y(2)=9/2
y(min)=y(1)=4
值域为:[4,9/2]