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A continuous function $f: R \rightarrow R$ satisfies the equation $f(x)=x+\int_{0}^{x} f(t) d t$.
Which of the following options is true ?
Options:
Which of the following options is true ?
Solution:
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Verified Answer
The correct answer is:
$f(x+y)=f(x)+f(y)+f(x) f(y)$
$f^{\prime}(x)=1+f(x) \quad f(0)=0$
$\frac{f(x)}{1+f(x)}=1$
$\ln (1+f(x))=x$
then $f(x+y)=f(x)+f(y) f(x) f(y)$
$\frac{f(x)}{1+f(x)}=1$
$\ln (1+f(x))=x$
then $f(x+y)=f(x)+f(y) f(x) f(y)$
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