A question about functions

ryu991

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May 14, 2015
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This is the question I am struggling with

if f(1) = 3 and f(n) = -2f(n-1) + 1 than f(5) = ???

I know the answer to the question is 43, I have no idea how it is 43, if someone can explain this to me it would be greatly appreciated.
 
This is the question I am struggling with

if f(1) = 3 and f(n) = -2f(n-1) + 1 than f(5) = ???

I know the answer to the question is 43, I have no idea how it is 43, if someone can explain this to me it would be greatly appreciated.
What have you tried? The policy of this forum is to help students with their problems, not simply solve it for them.

As a hint, what do you need to know to find f of any number? Look at the formula for the answer.
 
What have you tried? The policy of this forum is to help students with their problems, not simply solve it for them.

As a hint, what do you need to know to find f of any number? Look at the formula for the answer.

My issue is that I have literally no idea what to do, I know the answer is 43 because it is off of a regent review packet, but there is no explanation given. I figure that the n in the (n-1) is 5 but I have no idea what -2f even means so everything I have tried has been mostly gibberish. Can you tell me what -2f means in this instance?
 
My issue is that I have literally no idea what to do, I know the answer is 43 because it is off of a regent review packet, but there is no explanation given. I figure that the n in the (n-1) is 5 but I have no idea what -2f even means so everything I have tried has been mostly gibberish. Can you tell me what -2f means in this instance?
OK, can you find f(2)?
 
OK, can you find f(2)?

normally if i was asked to find f(2) I would substitiyte 2 into the equation and solve just like normally to find f(5) I would substitute 5 into the equation and solve. In this instance there are 2 variables

f(n) = -2f(n-1) + 1

If I have to find f(5) I would substitute like this

f(5) = -2f(5-1) + 1, that does absolutely nothing for me though, even if I simplify it I will get -8f +1 which doesn't seem to lead me anywhere. I am sure I am missing something with the -2f, but as I have absolutely no idea what -2f means in this instance I have no idea where I need to start.
 
My issue is that I have literally no idea what to do, I know the answer is 43 because it is off of a regent review packet, but there is no explanation given. I figure that the n in the (n-1) is 5 but I have no idea what -2f even means so everything I have tried has been mostly gibberish. Can you tell me what -2f means in this instance?
-2f(n-1) means -2 times f(n-1)
 
-2f(n-1) means -2 times f(n-1)

so if I do -2 tims f(n-1) + 1 and I am looking for f(5) than I would do -2 (5-1) + 1 which equals -7, the answer is -43, clearly I am missing something
 
so if I do -2 tims f(n-1) + 1 and I am looking for f(5) than I would do -2 (5-1) + 1 which equals -7, the answer is -43, clearly I am missing something
In -2 (5-1) + 1 what happened to the f?
I did not say that -2f(n-1)=-2(n-1).
 
In -2 (5-1) + 1 what happened to the f?
I did not say that -2f(n-1)=-2(n-1).

so I have to do -2 times f times n-1, I have no idea what the f is, I know the f is the function but I don't know what the function is.

I tried -2(n-1)(n-1) + 1 and when I did the math it did not get me the right answer, I have absolutely no idea what I would substitute for the f in this question, I tried changing the n to a 5, a 3, an n and a n-1, none of them got me the desired result and there is no other function listed so I have no idea what the f could be in the question.
 
I have no idea what the f could be in the question.
This is simply not true as you were told that f(n) = -2f(n-1) + 1.
Come on, just plug in 2 for n and let's see what you get. You CAN do this!
 
This is simply not true as you were told that f(n) = -2f(n-1) + 1.
Come on, just plug in 2 for n and let's see what you get. You CAN do this!

you said to substitute the function in for f, the problem is the function already has an f in it, so I don't get how that would get me to an answer

f(5) = -2f...
instead of f I type in the function so

-2(-2f(5-1)+1)(5-1) +1, that would still leave me with a random f that I have no idea how to get rid of or solve for.
 
you said to substitute the function in for f, the problem is the function already has an f in it, so I don't get how that would get me to an answer

f(5) = -2f...
instead of f I type in the function so

-2(-2f(5-1)+1)(5-1) +1, that would still leave me with a random f that I have no idea how to get rid of or solve for.
Just substitute 2 for n in f(n) = -2f(n-1) + 1 and report back with what you get. If you think math you may make a mistake. Just think that instead of writing n I will write 2 and I will not change ANY other detail at all.
 
Just substitute 2 for n in f(n) = -2f(n-1) + 1 and report back with what you get. If you think math you may make a mistake. Just think that instead of writing n I will write 2 and I will not change ANY other detail at all.

ok so...

-2f(2-1) +1

-4f+2f + 1

f(2) =-2f +1

like that?
 
ok so...

-2f(2-1) +1

-4f+2f + 1

f(2) =-2f +1

like that?
Of course not! f(n) is a function just like f(x). f(x) is NOT f times x!

Just write down f(n) = -2f(n-1) + 1 EXACTLY as it is except write 2 for n. Do not add. Do not subtract. Do not multiply. Just copy
 
Of course not! f(n) is a function just like f(x). f(x) is NOT f times x!

Just write down f(n) = -2f(n-1) + 1 EXACTLY as it is except write 2 for n. Do not add. Do not subtract. Do not multiply. Just copy

so

f(2) = -2f(2-1) +1
 
You should write the full equation. f(2)=-2f(1)+1. Do you know what f(1) equals? Hint, it was given! So what does f(2) equal?

f(2) = -2f(1) + 1, I know f(1) = 3, but how would I use that information to find f(2)? Would I put a 3 in for f? Is this a sequence? I am still extremely confused, sorry for my daftness.
 
f(2) = -2f(1) + 1, I know f(1) = 3, but how would I use that information to find f(2)? Would I put a 3 in for f? Is this a sequence? I am still extremely confused, sorry for my daftness.
You need to get a better grip on what an equal sign, = , means. It means that you can replace what is on the lhs of the equal sign with what is on the rhs of the equal sign and visa versa. So yes, replace f(1) with 3 and compute f(2).
f(n) is defined in terms of f(n-1), that is to get f(2) you need to know f(1); to get f(3) you need to know f(2); to get f(205) you need to know f(204).

You were given f(1). You now can compute f(2). Knowing f(2) you can then compute f(3). After finding f(3) you can find f(4) .....
 
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