Let f: R - 0,1 arrow R be a function such that f(x)+f((1/1-x))=1+x. Then f(2) is equal to

Question

Let f: R - 0,1 arrow R be a function such that f(x)+f((1/1-x))=1+x. Then f(2) is equal to (A) (7/3) (B) (9/2) (C) (9/4) (D) (7/4)

Tardigrade Admin · Accepted Answer

f ( x )+ f ((1/1- x ))=1+ x x =2 ⇒ f (2)+ f (-1)=3 (1) x =-1 ⇒ f (-1)+ f ((1/2))=0 (2) x =(1/2) ⇒ f ((1/2))+ f (2)=(3/2) (3) (1)+(3)-(2) ⇒ 2 f (2)=(9/2) ∴ f (2)=(9/4)

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

$\frac{7}{3}$

$\frac{9}{2}$

$\frac{9}{4}$

$\frac{7}{4}$

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

Q. Let f:R−{0,1}→R be a function such that f(x)+f(1−x1​)=1+x. Then f(2) is equal to

37​

29​

49​

47​