compositions of functions

[stargirl25]

Hi, i have this problem dealing with iteration. THe problem asks for the first four iterations of the funstion: f(n)=2f(n-1) if the initial value if f(1)=3. i tried to do it, but got that f(2)=5, when the answer in the book said it equaled 6.

 

[pka]

\(\displaystyle \L
f_1 = 3,\quad \Rightarrow \quad f_2 = 2f_{2 - 1} = 2f_1 = 2(3) = 6\).

 

[stargirl25]

i still dont get the rest of the answers right.

 

[pka]

You are having a problem with notation.
Here is the way it works:
\(\displaystyle \L
\begin{array}{l}
f(1) = 3 \\
n > 1\quad \Rightarrow \quad f(n) = 2f(n - 1) \\
f(2) = 2f(2 - 1) = 2f(1) = 2(3) = 6 \\
f(3) = 2f(3 - 1) = 2f(2) = 2(6) = 12 \\
\end{array}\)

 

[stargirl25]

is sort of get it,you have to plug in the product of (n-1) and f(?) into 2(f). I still didn´t get the last one, and thanks a bunch!

 

[stargirl25]

nevermind, i got it thank you so much!!!!!!!!!!!