Question

若f(x)满足3f(x-1)+2f(1-x)=2x,则f(x)=?

Answer 1

令 t= x-1 则 x=1+t

原式可为

3f(t) + 2f(-t)=2+2*t .(1)

将-t放入等式

3f(-t) + 2f(t) = 2 + 2 * (-t).(2)

(1)+(2) 得

5f(t) + 5f(-t) = 4 ---> f(t) + f(-t) = 4/5 -------(3)

(1)-(2) 得

f(t) - f(t) = 4t .(4)

(3) + (4) 得

2f(t)=4t + 4/5

所以

f(t)= 2t + 2/5

即

f(x)=2x+ 2/5