Let \(e\) be the base of natural logarithm and let \(f: \{1, 2, 3, 4\} \rightarrow \{1, e, e^2, e^3\}\) and \(g: \{1, e, e^2, e^3\} \rightarrow \left\{1, \dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}\right\}\) be two bijective functions such that \(f\) is strictly decreasing and \(g\) is strictly increasing. If \(\phi(x) = \left[f^{-1}\left\{g^{-1}\left(\dfrac{1}{2}\right)\right\}\right]^x\), then the area of the region \(R = \{(x, y): x^2 \leq y \leq \phi(x), 0 \leq x \leq 1\}\) is:

1. A \(\dfrac{3 - \log_e(2)}{3\log_e(2)}\)
2. B \(\dfrac{1}{3\log_e(2)}\)
3. C \(3 + \log_e(2)\)
4. D \(\dfrac{3 + \log_e(2)}{2 + \log_e(3)}\)