The limit doesn't exist (DNE).
Follow the pattern in the table. You have g (0.9) = 7, g (0.99) = 700, g (0.999) = 70,000 and so on. For every 10% increase in the value of x, the value of g(x) increases by a factor of 100. So as x gets closer to 1 (that is, as you add more 9s after the decimal point to x), g(x) will continue to increase by several magnitudes. The same thing effectively happens from the other side.
