The function $f(n) = 3f(n-2) - 2f(n-1)$, where $f(2) = 3$ and $f(1) = -1$. What is the value of $f(5)$?
Okay, so firstly we need to find an input to substitute for n to take advantage of the information we already have. If we let n=3 and plug in, we get
f(3)=3f(1) - 2f(2)
From that value, we can plug in the information we had into the equation, giving us
f(3)=3(-1) - 2(3) => f(3)= -9
Then, we repeat these steps. We now know the values of f(3), f(2), and f(1). Can you take it from there?
All the best.
Thank you for responding! Helped a lot. I also have another question:
Suppose the graph of $y=f(x)$ includes the points $(1,5),$ $(2,3),$ and $(3,1)$. Based only on this information, there are two points that must be on the graph of $y=f(f(x))$. If we call those points $(a,b)$ and $(c,d),$ what is $ab+cd$?
thanks so much!