F[f(x)]=x, and it increases monotonically. Get f- 1{f[f(x)]}=f(x), find the function of f(x) to get f[f(x)], and then find the inverse function of f- 1 {f(x)]} to return f(x).

The second analysis

F(x)=f- 1(x), because in f- 1{f[f(x)]

Then from the first analysis. f(x)=f- 1(x)

Another friend analyzed it. F(x)=f- 1(x) is a symmetric graph of f (x) = X.

If f(x)=f- 1(x), it means that f(x) is on this axis of symmetry.

Final analysis results. f(x)=x。

Good luck with your studies.