已知f(2x-1）=4x²-4x求f(x+1)

已知f(2x-1）=4x²-4x求f(x+1)
已知f(2x-1）=4x²-4x求f(x+1)

已知f(2x-1）=4x²-4x求f(x+1)
f(2x-1）=4x²-4x
设y = 2x-1,则 x = (y+1)/2;
f(2x-1）= f(y) = 4x²-4x = 4x*(x-1) = 4*(y+1)/2*((y+1)/2-1) = 2(y+1)(y-1)/2=y^2-1
所以f(x) = x^2-1;f(x+1) = (x+1)^2-1 = x^2+2x

f(2x-1）=4x²-4x=(2x-1)^2-1
f(x)=x^2-1
f(x+1)=(x+1)^2-1=x^2+2x

令2x-1=t
x=(t+1)/2
x+1=(t+3)/2
f(x+1)=4*[(t+3)/2]^2-4*(t+3)/2=t^2+4t+3
f(x+1)=x^2+4x+3

f(2x-1）=4x²-4x
令t=2x-1，则x=(t+1)/2
f(t) = 4*(t+1)^2/4 - 4*(t+1)/2 = t^2+2t+1-2t-2=t^2-1
将t换成x：
f(x) = x^2-1
f(x+1) = (x+1)^2-1 = x^2+2x