Let \( f(x) \) and \( g(x) \) be differentiable functions on \( (-\infty \), \( \infty) \) and l...

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Let \( f(x) \) and \( g(x) \) be differentiable functions on \( (-\infty \), \( \infty) \) and let \( f^{\prime}(x) \) and \( g^{\prime}(x) \) denote derivatives of \( f(x) \) and \( g(x) \) respectively. If \( f(0)=\frac{1}{2}, g(0)=\frac{1}{3}, f^{\prime}(0)=1 \) and \( g^{\prime}(0)=2 \), then the value of \( \lim _{x \rightarrow 0} \frac{2 f\left(2 x^{2}+3 x\right)-1}{3 g(x)-1} \) is
(a) 1
(b) \( \frac{1}{2} \)
(c) -1
(d) \( d \)
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