PL-OM 1992 Problem 4

The functions $f_0, f_1, f_2, ...$ are defined on the reals by $f_0(x) = 8$ for all $x$ , $f_{n+1}(x) = \sqrt{x^2 + 6f_n(x)}$ . For all $n$ solve the equation $f_n(x) = 2x$ .