Winter Mathematical Competition

a) Hint. Set $\frac{f(x)}{g(x)}=k$, where $k$ is a positive integer. Then $(2-k)x^2+(2+k)x-2(2+k)=0$ and use the fact that the discriminant of this quadratic equation is nonnegative.

Answer. $x=\frac{-3+\sqrt{33}}{2},\frac{-3-\sqrt{33}}{2},2$.

b) Answer. $x\in (-\infty ,-2]\cup [1,+\infty )$.