Let f(x) be a polynomial of degree 8 satisfying f(x)=1r,r=1,2,3,....9 and 9(x)=⎧⎪⎨⎪⎩(x−11)(x−22)(x−33−−−−(x−99)),n≠01+12+13+−−+19,n=0⎫⎪⎬⎪⎭ then value of ∣∣g(−1)f(10)∣∣ is

Let f(x) be a polynomial of degree 8 satisfying f(x)=1r,r=1,2,3,....9

1.	Let f(x) be a polynomial of degree 8 satisfying f(x)=1r,r=1,2,3,....9 and 9(x)=⎧⎪⎨⎪⎩(x−11)(x−22)(x−33−−−−(x−99)),n≠01+12+13+−−+19,n=0⎫⎪⎬⎪⎭ then value of ∣∣g(−1)f(10)∣∣ is
Answer» Let f(x) be a polynomial of degree 8 satisfying $f (x) = \frac{1}{r}, r = 1, 2, 3, . . . .9$ and $9 (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} (\frac{x - 1}{1}) (\frac{x - 2}{2}) (\frac{x - 3}{3} - - - - (\frac{x - 9}{9})), & n \neq 0 1 + \frac{1}{2} + \frac{1}{3} + - - + \frac{1}{9}, & n = 0 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭$ then value of $∣ ∣ \frac{g (- 1)}{f (10)} ∣ ∣$ is