Mathematics - Functions Question with Solution | TestHub

Let $g(x)$ be a polynomial of degree 8 satisfying $g(r)=\frac{1}{r}$, for $r=1,2,3,\dots ,9$, and

$$f(x)=\{\begin{array}{ll}\frac{\left(\frac{x}{1}-1\right)\left(\frac{x}{2}-1\right)\left(\frac{x}{3}-1\right)\dots \left(\frac{x}{9}-1\right)}{x}+\frac{1}{x},& x\ne 0\\ 1+\frac{1}{2}+\frac{1}{3}+\dots +\frac{1}{9},& x=0\end{array}$$

Then, calculate $\frac{f(-1)}{g(10)}$.