Question

If $f\left(x\right)=\log \left|\frac{1-x}{1+x}\right|$ then $f\left(a\right)+f\left(b\right)=$

Answer 1

$f\left(x\right)=log\frac{1-x}{1+x}f\left(a\right)+f\left(b\right)=log\frac{1-a}{1+a}+log\frac{1-b}{1+b}wecanusethatlogx+logy=logxyandlogx-logy=log\frac{x}{y}.Thenf\left(a\right)+f\left(b\right)=log(1-a)(1-b)-log(1+a)(1+b).alternativelyf\left(a\right)+f\left(b\right)=log\frac{(1-a)(1-b)}{(1+a)(1+b)}.$