SOLUTION: Consider the function f(x)=3x-5 and let f^n=fofofof..of where the composition is done n times. Find h(x)=f^n

Algebra ->  Functions -> SOLUTION: Consider the function f(x)=3x-5 and let f^n=fofofof..of where the composition is done n times. Find h(x)=f^n      Log On


   

Question 354516: Consider the function f(x)=3x-5 and let f^n=fofofof..of where the composition is done n times. Find h(x)=f^n
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
f^2(x)=3(3x-5)-5=3^2x-3*5-5

f^n(x)=3^n*x-3^(n-1)*5-5.

Verification by recurrence :

3*f^n(x)-5=3*3^n*x-3^n*5-5=3^(n+1)*x-3^n*5-5=f^(n+1)(x)