函数f(x)=Asinwx(w>0)对任意x有f(x-1/2)=f(x+1/2),且f(-1/4)=-a,那么f(9/4)为
问题描述：
函数f(x)=Asinwx(w>0)对任意x有f(x-1/2)=f(x+1/2),且f(-1/4)=-a,那么f(9/4)为
答
函数f(x)=Asinwx(w>0)对任意x有f(x-1/2)=f(x+1/2),且f(-1/4)=-a,那么f(9/4)为
解析：∵函数f(x)=Asinwx(w>0)对任意x有f(x-1/2)=f(x+1/2),且f(-1/4)=-a
令x=x-1/2代入得f(x-3)=f(x),
令x=x+3代入得f(x)=f(x+3),
∴T=3==>w=2π/3
f(x)=Asin(2π/3x)
f(-1/4)=Asin(-π/6)=-a==>A=2a
f(9/4)=2asin(2π/3*9/4)=-2a