Question

已知函数f(2x-1)=x2-3x+2,求f(x-2)

Answer 1

f(2x-1)=x^2-3x+2=(x-2)(x-1)

令t=2x-1

x=(t+1)/2

f(t)=[(t+1)/2-1][(t+1)/2-2]

=[(t-1)/2][(t-3)/2]

=(t-1)(t-3)/4

=(t^2-4t+3)/4

即f(x)=(x-1)(x-3)/4

f(x-2)=(x-2-1)(x-2-3)/4

=(x-3)(x-5)/4

=(x^2-8x+15)/4