Answer
Yes, we can conclude that $\displaystyle \lim_{x\rightarrow-\infty}\frac{f(x)}{g(x)}=2.$
Work Step by Step
If $\displaystyle \lim_{x\rightarrow\infty}\frac{f(x)}{g(x)}=2$, then we know that:
1. f and g have the same degree (say, n) and, after dividing both the numerator and denominator with $x^{n}$, we find that:
2. the leading coefficient of f is 2$\times$(leading coefficient of g)
If we want $\displaystyle \lim_{x\rightarrow-\infty}\frac{f(x)}{g(x)}$
we would also divide both the numerator and denominator with $x^{n} ,$
and the result will also be the ratio of the leading coefficients, 2.
