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

Pranav Ward 2022-09-14 Answered
How do you find the first three iterate of the function f ( x ) = 3 x 2 - 4 for the given initial value x 0 = 1 ?
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Answers (1)

coccusk7
Answered 2022-09-15 Author has 14 answers
Applying the function, we find:
x 1 = f ( x 0 ) = 3 x 0 2 - 4 = 3 ( 1 ) 2 - 4 = 3 - 4 = - 1
x 2 = f ( x 1 ) = 3 x 1 2 - 4 = 3 ( - 1 ) 2 - 4 = 3 - 4 = - 1
x 3 = f ( x 2 ) = 3 x 2 2 - 4 = 3 ( - 1 ) 2 - 4 = 3 - 4 = - 1
In fact, for any n 1 we have x n = - 1 , since:
f ( - 1 ) = 3 ( - 1 ) 2 - 4 = - 1
is a fixed point.

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