Prob. on function

1. Jun 18, 2012

mr newtein

1. The problem statement, all variables and given/known data
f(x) is a polynomial satisfying
f(x).f(1/x)=f(x)+f(1/x),f(3)=28 than f(4) is?

2. Relevant equations

3. The attempt at a solution
okay i have assumed a polynomial ,f(3) is given,so can i calculate coefficeints and degree of polynomial, and calculate f(4)

2. Jun 18, 2012

Contingency

f(1/x)=f(x)+f(1/x) => f(x)=0 for all x≠0
are you sure you copied correctly?

3. Jun 18, 2012

Staff: Mentor

How do you know the degree of the polynomial?

How does what you wrote apply to this problem? The OP wrote "f(x).f(1/x)=f(x)+f(1/x)", not f(1/x) = f(x) + f(1/x).

4. Jun 18, 2012

HallsofIvy

Staff Emeritus
Yes, but Contingency interpreted the "." as a period.

5. Jun 19, 2012

mr newtein

than whats the solution and question is correct.that dot is multiplication

6. Jun 19, 2012

Infinitum

By the PF rules, we cannot give you the solution. You have to do it yourself.

For starters, as Mark44 said, you cannot know the degree of the polynomial. So let it be a polynomial of degree n, with general coefficients. Now try finding the value of the function for a particular x, that will give you the sum of coefficients.

Using the relation $f(x)\cdot f(1/x) = f(x) + f(1/x)$ for your assumed polynomial, try to deduce what the function can be by comparing coefficients.

7. Jun 22, 2012

mr newtein

thanks bro i got the hint,and at last solution