Let (f: R -\\{0,1\\} \rightarrow R) be a function such that... | Mathematics | SolveeIt | Solveeit

Today, August 23

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

$\frac{9}{4}$

Explanation

Solution

f(x)+f(1−x1)=1+x
x=2⇒f(2)+f(−1)=3
x=−1⇒f(−1)+f(21)=0 (2)
x=21⇒f(21)+f(2)=23(3)
(1)+(3)−(2)⇒2f(2)=29
∴f(2)=49