# How do you find the first three iterate of the function #f(x)=3x^2-4# for the given initial value #x_0=1#?

##### 1 Answer

Nov 24, 2016

#### Explanation:

Applying the function, we find:

#x_1 = f(x_0) = 3x_0^2-4 = 3(1)^2-4 = 3-4 = -1#

#x_2 = f(x_1) = 3x_1^2-4 = 3(-1)^2-4 = 3-4 = -1#

#x_3 = f(x_2) = 3x_2^2-4 = 3(-1)^2-4 = 3-4 = -1#

In fact, for any

#f(-1) = 3(-1)^2-4 = -1#

is a fixed point.