# Thread: Function problem

1. ## 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?

2. ## Re: Function problem

I don't think you can derive it given the info you've presented.

3. ## Re: Function problem

I agree that you can't solve it. Are you sure you have given us all the information you have?

4. ## 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

5. ## Re: Function problem

how does making f a polynomial make f(n)= (n+ 7)/2

6. ## Re: Function problem Originally Posted by Ilikebugs 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 $f(4)=1$

7. ## Re: Function problem Originally Posted by Ilikebugs 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 $b$.