Question

设函数f(x)=x^2-1,对任意x∈[2/3,+∞),f(x/m)-(4m^2)f(x)≤f(x-1)+4f(m)恒成

Answer 1

(x^2)/(m^2)-1-4m^2(x^2-1)≤x^2-2x+4(m^2-1)

[1/(m^2)-4m^2-1]x^2≤-2x-3

4m^2-1/(m^2)+1≥3*(1/x)^2+2*(1/x)

令g(1/x)=3*(1/x)^2+2*(1/x)

(1/x)∈(0,2/3]

4m^2-1/(m^2)+1≥g(1/x)max=g(2/3)=8/3

m^2≥3/4

m≤-√(3)/2或m≥√(3)/2