Question

已知函数f(x)=(x-1)/(x+2).x属于[3,5].(1)判断函数f(x)的单调性,并证明

Answer 1

函数f(x)=(x-1)/(x+2)
=1-3/（x+2).x属于[3,5].
增函数
3<=u<v<=5
f(u)-f(v)
=3/(v+2)-3/(u+2)
=3(u-v)/(u+2)(v+2)<0
f(u)<f(v)