# How do you find the first three iterates for the function f(x)=x^2+2 given the initial value x_0=-1?

Jan 22, 2017

See explanation.

#### Explanation:

Is it the iteration

${x}_{n} = {x}_{n - 1}^{2} + 2 , n = 1 , 2 , 3 , . . ,$ with x_0=-1?

Such iterations $m i g h t$ lead to

limit ${x}_{n}$ = a zero of f(x)=0, as $n \to \infty$.

Yet, in this case, there is no real solution at all..