Question

设f(x)=loga(1-x)/(1+x),a>0,a≠1 求证对任意的m,n∈(-1,1)f(m)+f(n)=f[(m

Answer 1

f(m) + f(n) = loga(1-m)/(1+m) + loga(1-n)/(1+n)

= loga[(1-m)(1-n)]/[(1+m)(1+n)]

=loga[1+mn - m - n]/[1+mn+m+n]

=loga[ 1 - (m+n)/(1+mn)]/[1 + (m+n)/(1+mn)]

= f[(m+n)/(1+mn)]

证毕.