Question

f(x)= 1-x/1+x prove that
f(x) * f(y) = f(x+y/1+xy)​

Answer 1

LHS=RHS

Step-by-step explanation:

f(x)=log[1+x1−x]so, f(y)=log[1+y1−y]Consider, LHS=f(x)+f(y)=log[1+x1−x]+log[1+y1−y]=log(1+x)−log(1−x)+log(1+y)−log(1−y) [log(mn)=logm−logn]=log(1+x)+log⎛⎝1+y⎞⎠−[log(1−x)+log(1−y)]=log[(1+x)(1+y)]−log[(1−x)(1−y)]=log(1+x+y+xy)−log(1−y−x+xy)=log(1+x+y+xy1−y−x+xy)RHS= f(x+y1+xy)=log⎡⎣1+x+y1+xy1−x+y1+xy⎤⎦=log⎡⎣1+xy+x+y1+xy1+xy−x−y1+xy⎤⎦=log[1+xy+x+y1+xy−x−y]So, LHS=RHSHence proved