Question

if f(x) =log(1+x/1-x),then show that f(x) +f(y) =f(x+y/1+xy)
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Answer 1

$\huge \bold {\red {\mid{\underline { \overline{\mathfrak{ANSWER}}}}}} \mid$

$\star \: \: \underline \blue{given} \blue{ : }$

$\bold{f(x) = log( \frac{1 + x}{1 - x} ) }$

$\bold{f(y) = log( \frac{1 + y}{1 - y} ) }$

$\star \: \: \underline \blue{solution} \blue{ : }$

$f(x) + f(y)$

$\longrightarrow \: log( \frac{1 + x}{1 - x} ) + log( \frac{1 + y}{1 - y} )$

$\longrightarrow \: log( \frac{1 + x + y + xy}{1 - x - y + xy} )$

$\longrightarrow \: log( \frac{(x + y) + (1 + xy)}{ - (x + y) + (1 + xy)} )$

$\longrightarrow \: \boxed {\mathfrak{f( \frac{x + y}{1 + xy} )}}$

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