Question

Let $f: R -\{0,1\} \rightarrow R$ be a function such that $f(x)+f\left(\frac{1}{1-x}\right)=1+x$. Then $f(2)$ is equal to

• A. $\frac{7}{3}$
• B. $\frac{9}{2}$
• C. $\frac{9}{4}$
• D. $\frac{7}{4}$

Answer 1

Answer: (C)

$ f ( x )+ f \left(\frac{1}{1- x }\right)=1+ x$
$ x =2 \Rightarrow f (2)+ f (-1)=3 $(1)
$ x =-1 \Rightarrow f (-1)+ f \left(\frac{1}{2}\right)=0 $ (2)
$ x =\frac{1}{2} \Rightarrow f \left(\frac{1}{2}\right)+ f (2)=\frac{3}{2} $(3)
$ (1)+(3)-(2) \Rightarrow 2 f (2)=\frac{9}{2} $
$ \therefore f (2)=\frac{9}{4}$