The math problem in the college entrance examination is urgent.

It is known that the function f(x) satisfies f(x)=2f(2-x)-x on r? +8x-8，

Find the equation of curve tangent at (1, f( 1)).

Substituting x=2-t into the condition satisfied by f(x), we get:

f(2-t)=2f(2-(2-t))-(2-t)？ +8(2-t)-8，

That is, f(2-t)=2f(t)-t? -4t+2……( 1)

Substituting x=t into the condition satisfied by f(x), we get:

f(t)=2f(2-t)-t？ +8t-8……(2)

(1) is substituted into (2) to obtain:

f(t)=2(2f(t)-t？ -4t+2)-t？ +8t-8

F(t)=t? +4/3

So f(x)=x? +4/3

f( 1)=7/3

f？ (x)=2x，f？ ( 1)=2

So the tangent equation is y-7/3=2(x- 1),

That is 6x-3y+ 1=0.