\textbf{119-} The function $f(x) = \dfrac{|2x+1|+2x}{|x|+b}$ has two oblique asymptotes and each root of the function is excluded from the domain of the function. If the limit of the function as $x \to 1^+$ is finite, what is $\displaystyle\lim_{x \to 1^+} f(x)$?
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(1) $-3$ \hfill (2) $1$ \hfill (3) $-\dfrac{1}{2}$ \hfill (4) $\dfrac{1}{2}$
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