Dear Student, fx= ln1-x1+xNow fx+fy= fx+y1+xy ln1-x1+x+ ln1-y1+y= ln ln1-x+y1+xy1+x+y1+xy= ln1+xy-x-y1+x+y+xyln1-x1-y1+x1+y= ln1+xy-x-y1+x+y+xy1-x1-y1+x1+y= 1+xy-x-y1+x+y+xy1-y-x+xy1+x+xy+y= 1+xy-x-y1+x+y+xy1 =1 So all values of x and y will satisy the equation Regards

plz solve 4th

Dear Student, f (x) = \ln (\frac{1 - x}{1 + x}) Now f (x) + f (y) = f (\frac{x + y}{1 + xy}) \ln (\frac{1 - x}{1 + x}) + \ln (\frac{1 - y}{1 + y}) = \ln \ln (\frac{1 - \frac{x + y}{1 + xy}}{1 + \frac{x + y}{1 + xy}}) = \ln (\frac{1 + xy - x - y}{1 + x + y + xy}) \ln (\frac{(1 - x) (1 - y)}{(1 + x) (1 + y)}) = \ln (\frac{1 + xy - x - y}{1 + x + y + xy}) \frac{(1 - x) (1 - y)}{(1 + x) (1 + y)} = \frac{1 + xy - x - y}{1 + x + y + xy} \frac{1 - y - x + xy}{1 + x + xy + y} = \frac{1 + xy - x - y}{1 + x + y + xy} 1 = 1 So all values of x and y will satisy the equation . Regards

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