Question

若f(x)满足3f(x-1)-2f(1-x)=2x,求函数f(x)的解析式

Answer 1

令x-1=t
3f(t)-2f(-t)=2t+2
3f(-t)-2f(t)=-2t+2
带入消元
f(t)=2t/5+2
即 f(x)=2x/5+2

Answer 2

令t=x-1
x=t+1
代人得
3f(t)-2f(-t)=2t+2
即
3f(x)-2f(-x)=2x+2
又有3f(-x)-2f(x)=-2x+2
两式消去f(-x)得
13f(x)=2x+10
f(x)=(2x+10)/13

Answer 3

令t=x-1
x=t+1
代人得
3f(t)-2f(-t)=2t+2┈┈①
令t=1-x
x=1-t
代人得
3f(-t)-2f(t)=2-2t┈┈②
①*3+②*2得 f(t)=2t/5+2