Question 45

Let $$f:R \rightarrow R$$ and $$g:R \rightarrow R$$ be functions satisfying
$$f(x + y)=f(x)+f(y)+f(x)f(y)$$ and $$f(x) = xg(x)$$
for all $$๐‘ฅ, ๐‘ฆ \in R$$. If $$\lim_{x \rightarrow 0} g(x) = 1$$, then which of the following statements is/are TRUE?


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