函数f(x)=2sin(-3x+π/4)
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函数f(x)=2sin(-3x+π/4)
(1)求f(x)的单调增区间
(2)当f(x)≥√2时,求x的取值范围
(1)求f(x)的单调增区间
(2)当f(x)≥√2时,求x的取值范围
1、将函数利用诱导公式把x的系数化为正数,f(x)=-2sin(3x-π/4),现在只需找到sin(3x-π/4)的递减区间即可.
令3x-π/4=t,则在π/2+2kπ《t《3π/2+2kπ,k属于z上,sint递减
即π/2+2kπ《3x-π/4《3π/2+2kπ
求出上式关于x的不等式即为函数的单调增区间【π/4+2kπ/3,7π/12+2kπ/3】,k属于z
2、2sin(-3x+π/4)≥√2,则sin(-3x+π/4)≥√2/2
即π/4+2kπ《3x-π/4《3π/4+2kπ,解得x的取值范围为【π/6+2kπ/3,π/3+2kπ/3】
令3x-π/4=t,则在π/2+2kπ《t《3π/2+2kπ,k属于z上,sint递减
即π/2+2kπ《3x-π/4《3π/2+2kπ
求出上式关于x的不等式即为函数的单调增区间【π/4+2kπ/3,7π/12+2kπ/3】,k属于z
2、2sin(-3x+π/4)≥√2,则sin(-3x+π/4)≥√2/2
即π/4+2kπ《3x-π/4《3π/4+2kπ,解得x的取值范围为【π/6+2kπ/3,π/3+2kπ/3】
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