Question

若不等式组2x-a小于1和x-2b大于3的解集为x小于负1大于1，则（a+1）（b-1）的值为

Answer 1

2x-a<1
x<(a+1)/2

x-2b>3
x>2b+3
所以2b+3<x<(a+1)/2
解集是-1<x<1
所以2b+3=-1
(a+1)/2=1
b=-2,a=1
所以(a+1)(b-1)=2×(-3)=-6

Answer 2

若sinx<=cosx
则2kπ-3π/4<=x<=2kπ+π/4
sinx在(2kπ-3π/4,2kπ-π/2)递减(2kπ-π/2,2kπ+π/4)递增
所以-1<=sinx<=√2/2
此时y=sinx
所以-1<=y<=√2/2

同理
若sinx>cosx
则2kπ+π/4<=x<=2kπ+5π/4
cosx在(2kπ+π/4,2kπ+π)递减,(2kπ+π,2kπ+5π/4)递增
所以-1<cosx<√2/2
此时y=cosx
所以-1<y<√2/2

所以值域[-1,√2/2]