Question

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)?

Answer 1

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

Answer 2

nopes its not that

Answer 3

Is that the whole question?

Answer 4

yup !!

Answer 5

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,

Answer 6

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).

Answer 7

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.

Answer 8

Does this help?

Answer 9

yes,
thanks

Answer 10

No probs.