Suppose \( f(x) \) and \( g(x) \) are two continuous functions defined for \( 0 \leq x \leq 2 \)...

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Suppose \( f(x) \) and \( g(x) \) are two continuous functions defined for \( 0 \leq x \leq 2 \)
Given \( f(x)=\int_{0}^{1} e^{x+t} \cdot f(t) d t \) and \( g(x)=\int_{0}^{1} e^{x+t} \cdot g(t) d t+x \)
The value of \( \frac{g(0)}{g(2)} \) equals :
(a) 0
(b) \( \frac{1}{3} \)
(c) \( \frac{1}{e^{2}} \)
(d) \( \frac{2}{e^{2}} \)
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