CAT 2002 — QA Question 17

$$\begin{gathered} f\left(x\right)+f\left(y\right)=\log \left(\frac{1+x}{1-x}\right)+\log \left(\frac{1+y}{1-y}\right) \\ =\log \frac{\left(1+x\right)(1+y)}{\left(1-x\right)(1-y)} \\ =\log \frac{1+xy+x+y}{1+xy-(x+y)} \\ = \log \frac{1+{\displaystyle \frac{x+y}{1+xy}}}{1-{\displaystyle \frac{x+y}{1+xy}}} \\ =f\left(\frac{x+y}{1+xy}\right) \end{gathered}$$

Hence, option (d).