SOLUTION: Let f(x)=2x+3 and g(x)=x^2 Determine the formula for the following composition: (g o g o g...o g)(x) where there are n copies of the function g This is a complete mystery

Algebra ->  Functions -> SOLUTION: Let f(x)=2x+3 and g(x)=x^2 Determine the formula for the following composition: (g o g o g...o g)(x) where there are n copies of the function g This is a complete mystery      Log On


   

Question 984759: Let f(x)=2x+3 and g(x)=x^2
Determine the formula for the following composition:
(g o g o g...o g)(x) where there are n copies of the function g
This is a complete mystery o me, not even sure where to start.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look for how you can deduce the pattern.
Start with n=2
g%28x%29og%28x%29=%28x%5E2%29%5E2=x%5E4
.
.
.
n=3
g%28x%29og%28x%29og%28x%29=%28x%5E2%29%5E4=x%5E8
.
.
.
n=4
g%28x%29og%28x%29og%28x%29og%28x%29=%28x%5E2%29%5E8=x%5E16
So the exponent is increasing as 2%5En
So for n copies,
G%5Bn%5D%28x%29=x%5E%282%5En%29
where
G[n]=g(x) o g(x) o g(x) ... g(x) <--- n times