Q. Compute by the method of fixed point iteration a real root of the equation x^3 + x^2 - 1 =0 correct up to two decimal places.

In the above problem if we take f(x)=0, then to solve it we can write f(x) in the form of x=g(x). Now g(x) can take three different forms.

i) 1/sqrt(1+x)

ii) 1/x+x^2

iii) -1+ (1/x^2)

Now my question is, for which form of g(x) I can be sure that the obtained root converges to the actual root?