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- anonymous

F(x) is a polynomial of 8 degree
f(K)=1/k
K=1,2,3,4,5,6,7,8,9
find F(10)?

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- anonymous

F(x) is a polynomial of 8 degree
f(K)=1/k
K=1,2,3,4,5,6,7,8,9
find F(10)?

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- anonymous

Replace K with 10
f(10)=1/10

- anonymous

nopes its not that

- anonymous

Is that the whole question?

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- anonymous

yup !!

- anonymous

Jai, I think what you're being asked to do is recognize this:
You are told you have a polynomial of degree 8 which you have to find. So you have\[f(x)=a_8x^8+a_7x^7+...+a_1x+a_0\]Being asked to find the polynomial is the same as saying, "Find the coefficients above."
You're told that, at the points x=1 to 9, the function f(x) is equal to 1/x; that is, \[\frac{1}{x}=a_8x^8+a_7x^7+...+a_1x+a_0\]for x=1,2,...,9.
So,

- anonymous

for x=1,\[\frac{1}{1}=1=a_8(1)^8+a_7(1)^7+...+a_1(1)+a_0\]that is,\[1=a_8+a_7+...+a_1+a_0\]This is one (linear) equation.
You repeat the process for the other eight numbers and you'll have nine linear equations in nine unknowns. Those unknowns are the coefficients. You can solve this system exactly for those coefficients. You'll then have the polynomial.
Once you have the polynomial, you can use it to calculate f(10).

- anonymous

It's turgid algebra. If you don't have to show how you've solved for the coefficients, I would demonstrate that you can set the problem up, and illustrate how you solve it (e.g. matrices). Then look for an online matrix calculator to solve the system. Doing it by hand will take a long time, and there's so much room for error.

- anonymous

Does this help?

- anonymous

yes,
thanks

- anonymous

No probs.

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