find-f-x-if-f-1-x-f-1-x-x-

Question Number 68260 by aliesam last updated on 08/Sep/19

f i n d f (x) i f

f (\frac{1}{x}) + f (1 - x) = x

Commented by Prithwish sen last updated on 08/Sep/19

Put x = \frac{1}{x} \Rightarrow f (x) + f (1 - \frac{1}{x}) = \frac{1}{x} \dots \dots (i)

Putx = \frac{x}{x - 1} \Rightarrow f (1 - \frac{1}{x}) + f (\frac{1}{1 - x}) = \frac{x}{x - 1} \dots . . (ii)

Putx = 1 - x \Rightarrow f (\frac{1}{1 - x}) + f (x) = 1 - x \dots . . (iii)

(i) - (ii) + (iii) we get

f (x) = \frac{1}{2} [\frac{1}{x} - \frac{x}{x - 1} + 1 - x] please check .