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Thread: Function problem

  1. #1
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    Function problem

    If f(3)=5,f(n)=f(n-2)+1 then what is f(4)? I don't know how to get f(4) because the function only gives an odd x value?
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  2. #2
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    Re: Function problem

    I don't think you can derive it given the info you've presented.
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  3. #3
    Junior Member Walagaster's Avatar
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    Re: Function problem

    I agree that you can't solve it. Are you sure you have given us all the information you have?
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  4. #4
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    Re: Function problem

    IF you add the condition that f is a polynomial, then f(n)= (n+ 7)/2 so that f(4)= 11/2
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    Re: Function problem

    how does making f a polynomial make f(n)= (n+ 7)/2
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    Re: Function problem

    Quote Originally Posted by Ilikebugs View Post
    how does making f a polynomial make f(n)= (n+ 7)/2
    Examine $f(n)=.5n+3.5$. Does $f(3)=5~?$

    Look at this page. You must scroll down to see the final answer. $f(4)=0$

    Note that from the given
    $ \begin{align*}f(3) &=5 \\\text{so that if }f(n)&=f(n-2)+1\\f(3)=&5=f(1)+1\\f(1)&=4 \end{align*}$

    Now look at this page.
    See a different but perfectly good solution where $f(4)=1$
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  7. #7
    Junior Member Walagaster's Avatar
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    Re: Function problem

    Quote Originally Posted by Ilikebugs View Post
    how does making f a polynomial make f(n)= (n+ 7)/2
    With the given recurrence you know it can't be more than a first degree polynomial. So assume $f(n) = an + b$ and apply what you are given to get $a$ and $b$.
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