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The function $f(n) = 3f(n-2) - 2f(n-1)$, where $f(2) = 3$ and $f(1) = -1$. What is the value of $f(5)$?

 Feb 12, 2021
 #1
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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.

BasicMaths

 Feb 12, 2021
 #2
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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!

 Feb 12, 2021
 #3
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ab + cd = 18.

Guest Feb 14, 2021

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