College

A sequence is defined by the recursive function [tex]f(n+1) = f(n)[/tex]. If [tex]f(3) = 9[/tex], what is [tex]f(1)[/tex]?

A. 1
B. 3
C. 9
D. 81

Answer :

To solve this problem, we need to understand what the recursive function [tex]$f(n+1) = f(n)$[/tex] means. This equation tells us that the function [tex]$f(n)$[/tex] produces the same value for every input [tex]$n$[/tex]. In other words, [tex]$f(n)$[/tex] is a constant function.

Now, we are given that [tex]$f(3) = 9$[/tex]. Since the function is constant, this same value of 9 applies to all [tex]$n$[/tex]. Therefore, [tex]$f(n)$[/tex] is equal to 9 for any [tex]$n$[/tex].

So, when we are asked to find [tex]$f(1)$[/tex], we can conclude that because [tex]$f(n)$[/tex] is constant for all values of [tex]$n$[/tex], [tex]$f(1)$[/tex] will also be 9.

Therefore, the answer is:
9