Question

设f(x+1)=x^2-3x+2,求f(x)的解析式

Answer 1

令a=x+1,则x=a-1
f(a)=(a-1)^2-3(a-1)+2=a^2-5a+6
f(x)=x^2-5x+6

Answer 2

x^2-3x+2
=(x-1)(x-2)
x1=1,x2=2

因此f(x)=1+1=2或2+1=3

Answer 3

f(x+1)=x^2-3x+2=(x+1)^2-5(x+1)+6
f(x)=x^2-5x+6

Answer 4

2f(x)+f(1/x)=x (1)
令x=1/x,
得2f(1/x)+f(x)=1/x (2)
(1)*2-(2)得，3f(x)=2x-1/x
f(x)=2x/3-1/3x