1. let t = x-1/x→→→→ T2 = x2+1/x2-2, →→→→→→→→→→→ T2+2 = (x4+1)/x2 →

So f (t) = 1/(t 2+2), that is, f (x) = 1/(x 2+2).

2. let x^2 /x^2 -2=t 2 = t 2 = t, →→→→→1/t = (x 2-2)/x 2 =1-2/x 2, →→→→1/x.

→→x^2=2t/(t- 1)→→x^2- 1= t+ 1/t- 1 .

So f (x 2-1) = f (t+1/t-1) = LG (t), that is, f(x+ 1 /x- 1)=lg(x).

And because f(g(x))=lgx, so g(x)= x+ 1 /x- 1.

3. Let f( f(x)/ f(x)- 1), the third question is incomplete and cannot be answered. Please complete the supplement. The three questions asked by the landlord should be of the same type, that is, variable substitution method.

May you learn from the next level.