f(x)=-X²+4x
=-(x²-4x)
=-(x²-4x+4)+4
=-(x-2)²+4
x∈[1,2],单调递增
x∈[2,4）单调递减
当x=2时,f(x)=4
当x=4时,f(x)=0
∴f(x)的值域﹙0,4]