1.设f(x)=kx+b
3f(x+1)=3kx+3k+3b
2f(x-1)=2kx-2k+2b
3f(x+1)-2f(x-1)=(3kx+3k+3b)-(2kx-2k+2b)=kx+5k+b=2x+17;
所以：k=2
5k+b=17,b=7
所以函数解析式f(x)=2x+7
2.f(x)=f(x-y)+y(2x-y+1)
f(0)=f(-y)+y(-y+1)=1
f(-y)=1-y(-y+1)
f(y)=1+y(y+1)=y^2+y+1
所以函数解析式f(x)=x^2+x+1
3.f(x+1/x)=x^3+1/x^3=(x+1/x)(x^2+1/x^2-1)
令x+1/x=t,t^2=x^2+1/x^2+2,x^2+1/x^2=t^2-2
所以 f(x+1/x)=x^3+1/x^3=(x+1/x)(x^2+1/x^2-1)
可化为：f(t)=t(t^2-2-1)=t^3-3t
所以函数解析式为：f(x)=x^3-3x