f(x)=sin(x-π/4)+3cos(x+π/4)
=-cos（π/2+x-π/4)+3cos(x+π/4)
=-cos(x+π/4)+3cos(x+π/4)
=2cos(x+π/4)
π+2kπ≤x+π/4≤2π+2kπ
3π/4+2kπ≤x≤7π/4+2kπ