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  • $\begingroup$ I edited the LaTeX so that it matches your description. Previously it said $f_{n-1}(x/y=(3+y)/2)$. Hopefully I didn't add any errors... $\endgroup$ Commented Jan 3, 2014 at 5:59
  • $\begingroup$ It might be clearer to replace $y$ by $t$. Isn't $f_1(1)=\frac{1+\sqrt{17}}{4}\approx 2.28$? $\endgroup$ Commented Jan 3, 2014 at 6:52
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    $\begingroup$ so $$f_2(x)=2+\frac{\sqrt [3]{-1+2\,x+2\,\sqrt {-x+{x}^{2}}}}{2}+\frac {1}{2\sqrt [3]{-1+2\,x+2\,\sqrt {-x+{x}^{2}}}}$$ but $f_3$ is not going to be pretty. $\endgroup$ Commented Jan 3, 2014 at 8:27