Пусть f(x)=x-1/x+1. Докажите, что:

Решите задачу:

$a) f(x)*f(-x)= \frac{x-1}{x+1} * \frac{(-x)-1}{(-x)+1} = \frac{(x-1)*(-x-1)}{(x+1)(-x+1)} = \frac{-(x-1)(x+1)}{-(x+1)(x-1)} =1 \\b)f( \frac{1}{x} )= \frac{ \frac{1}{x}-1 }{ \frac{1}{x} +1} = \frac{ \frac{1-x}{x} }{ \frac{x+1}{x} } = \frac{1-x}{x+1} = -\frac{x-1}{x+1} =-f(x)$
$c) f(- \frac{1}{x} )*f(x)= \frac{ -\frac{1}{x}-1 }{ -\frac{1}{x} +1}*\frac{x-1}{x+1}= \frac{ \frac{-1-x}{x}}{ \frac{-1+x}{x} } *\frac{x-1}{x+1}= \frac{-1-x}{-1+x} *\frac{x-1}{x+1}=\\= \frac{-(x+1)}{x-1} *\frac{x-1}{x+1}=- \frac{(x+1)(x-1)}{(x-1)(x+1)} =-1 \\d)f( \frac{1}{x} )*f(-x)= \frac{ \frac{1}{x}-1 }{ \frac{1}{x} +1}* \frac{-x-1}{-x+1} = \frac{1-x}{x+1}* \frac{-(x+1)}{-(x-1)} = -\frac{(x-1)(x+1)}{(x+1)(x-1)} =-1$