已知f(2x+1)=x^2-2x,求f(x)与f(2x-1)的解析式

2024-12-28 19:50:55
推荐回答(2个)
回答1:

f(2x+1)=x^2-2x
令t=2x+1,则x=(t-1)/2
f(t)=[(t-1)/2]²-2(t-1)/2=(t-1)²/4-(t-1)
所以f(x)=(x-1)²/4-(x-1)
f(2x-1)=(2x-1-1)²/4-(2x-1-1)=(x-1)²-(2x-2)=x²-4x+3

回答2:

解:设 t=2x+1, 则x=(t-1)/2
f(t)=(t-1)^2/4-t+1
所以:
f(x)=(x-1)^2/4-x+1
f(2x-1)=(2x-1-1)^2/4-(2x-1)+1
=(x-1)^2-2x+2