f-x-2f-1-2-3x-2-f-x-

Question Number 114586 by Khalmohmmad last updated on 19/Sep/20

f (x) - 2 f (\frac{1}{2}) = 3 x - 2

f (x) = ?

Commented by Dwaipayan Shikari last updated on 19/Sep/20

f (x) - 2 f (\frac{1}{x}) = 3 x - 2 \to (a)

f (\frac{1}{x}) - 2 f (x) = \frac{3}{x} - 2

2 f (\frac{1}{x}) - 4 f (x) = \frac{6}{x} - 4 \to (b)

- 3 f (x) = 3 x + \frac{6}{x} - 6

f (x) = 2 - x + \frac{2}{x}

Commented by Aziztisffola last updated on 19/Sep/20

f (\frac{1}{2}) or f (\frac{1}{x}) ?

Answered by Olaf last updated on 19/Sep/20

f (x) = 3 x - 2 + 2 f (\frac{1}{2}) (1)

for x = \frac{1}{2} :

f (\frac{1}{2}) - 2 f (\frac{1}{2}) = 3 \frac{1}{2} - 2 = - \frac{1}{2}

- f (\frac{1}{2}) = - \frac{1}{2}

f (\frac{1}{2}) = \frac{1}{2}

(1) : f (x) = 3 x - 2 + 2 (\frac{1}{2}) = 3 x - 1

f (x) = 3 x - 1

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