If f(x)=log[1+x/1-x], then show that f(x)+f(y)=f(x+y/1+xy).

Dear student
fx=log1+x1-xso, fy=log1+y1-yConsider, LHS=fx+fy=log1+x1-x+log1+y1-y=log1+x-log1-x+log1+y-log1-y     logmn=logm-logn=log1+x+log(1+y)-log1-x+log1-y=log1+x1+y-log1-x1-y=log1+x+y+xy-log1-y-x+xy=log1+x+y+xy1-y-x+xyRHS= fx+y1+xy=log1+x+y1+xy1-x+y1+xy=log1+xy+x+y1+xy1+xy-x-y1+xy=log1+xy+x+y1+xy-x-ySo, LHS=RHSHence proved
Regards

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