2. RP Linear Guess

By examining a plot of sqrt(f) for 0.5 <= f < 2.0:

we may guess at a pretty good linear approximation which is exact for f=2, and has a g-axis intercept of 0.5:
  g = 0.5 + f*(sqrt(2)-0.5)/2

  g = 0.5 + f*0.45710678118654757