函数f(X)=asin(2x+pi/6)+2a+b的定义欲为 [0,Pi/2]值遇为[-5,+1]求a和b

0<=x<=π/2
0*2+π/6<=2x+π/6<=2*π/2+π/6
π/6<=2x+π/6<=7π/6
所以2x+π/6=π/2，sin(2x+π/6)=1
2x+π/6=7π/6，sin(2x+π/6)=-1/2
所以-1/2<=sin(2x+π/2)<=1

若a>0,则sin(2x+π/2)=1，最大=a+2a+b=1
sin(2x+π/2)=-1/2，最小=-a/2+2a+b=-5
a=4，b=-11

若a<0,则sin(2x+π/2)=-1/2，最大=-a/2+2a+b=1
sin(2x+π/2)=1，最小=a+2a+b=-5
a=-4，b=7

若a=0,则f(x)=b,值域不是[-5,+1]

所以a=4,b=-11或a=-4,b=7