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
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
