\textbf{15.} $f$ is a homographic function, $g(x) = \dfrac{1}{f(x)}$, and $\displaystyle\lim_{x \to -\infty} \dfrac{f(x)}{g^{-1}(x)} = \lim_{x \to +\infty} \dfrac{g^{-1}(x)}{g(x)}$. What value can $\displaystyle\lim_{x \to 0^+} f^{-1}(x)$ be?
\[
\text{(1) zero} \qquad \text{(2) } \dfrac{1}{2} \qquad \text{(3) } 1 \qquad \text{(4) } 2
\]