Solve Polynomial Function: f(x) with f(3)=28, Find f(4)

[mr newtein]

Homework Statement

f(x) is a polynomial satisfying
f(x).f(1/x)=f(x)+f(1/x),f(3)=28 than f(4) is?

Homework Equations

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)

 

[Contingency]

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

 

[Mark44]

Homework Statement

f(x) is a polynomial satisfying
f(x).f(1/x)=f(x)+f(1/x),f(3)=28 than f(4) is?

Homework Equations

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)

How do you know the degree of the polynomial?

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

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).

 

[HallsofIvy]

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

 

[mr newtein]

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

than what's the solution and question is correct.that dot is multiplication

 

[Infinitum]

than what's the solution and question is correct.that dot is multiplication

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.

 

[mr newtein]

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.

thanks bro i got the hint,and at last solution