How do you find the first three iterate of the function f(x)=3x+5 for the given initial value x_0=−4?

genestesya

genestesya

Answered question

2022-09-04

How do you find the first three iterate of the function f ( x ) = 3 x + 5 for the given initial value x 0 = - 4 ?

Answer & Explanation

shosautesseleol

shosautesseleol

Beginner2022-09-05Added 16 answers

Although I've never really seen it phrased in this way, I believe the iterations to mean:
XXX x 1 = f ( x 0 ) 
XXX x 2 = f ( x 1 ) 
XXX x 3 = f ( x 2 ) 
...and so on

Given that this is the case f ( x ) = 3 x + 5 and x 0 = - 4 ,
we have:
XXX x 1 = f ( - 4 ) = 3  ( - 4 ) + 5 = - 12 + 5 = - 7 
XXX x 2 = f ( - 7 ) = 3  ( - 7 ) + 5 = - 21 + 5 = - 16 
XXX x 3 = f ( - 16 ) = 3  ( - 16 ) + 5 = - 48 + 5 = - 43 
( x 1 , x 2 , x 3 ) = ( - 7 , - 16 , - 43 ) 

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