1)f(x)的定义域为R;
2)f(-x)=|sin(-2x)|+|cos(-2x)|=|sin2x|+|cos2x|=f(x)
f(x)为偶函数
3)f(x+π/4)= |sin(2x+π/2)|+|cos(2x+π/2)| = |cos2x|+|sin2x| =f(x)
f(x)是周期为π/4的周期函数;
4)当x∈[0,π/4]时,f(x)=√2sin(2x+π/4)
值域为[1,√2]
5)可作出f(x)图象可知
f(x)的增区间为[kπ/4,π/8+kπ/4](k∈Z),
f(x)的减区间为[π/8+kπ/4,π/4+kπ/4]
追问不好意思,我已经选了满意答案了。