y-f-xy-f-x-x-y-R-If-f-4-1006-so-f-2012-

Question Number 10170 by Joel575 last updated on 28/Jan/17

y . f (x y) = f (x) x, y \in R

If f (4) = 1006, so f (2012) = ?

Answered by ridwan balatif last updated on 28/Jan/17

f (xy) = \frac{f (x)}{y}, f (4) = 1006

if x = 1 y = 4, then

f (1.4) = \frac{f (1)}{4}

f (4) = \frac{f (1)}{4}

1006 = \frac{f (1)}{4}

4 = \frac{f (1)}{1006}

f (1.1006) = 4

f (1006) = 4

if x = 2 y = 2

f (2.2) = \frac{f (2)}{2}

f (4) = \frac{f (2)}{2}

2 = \frac{f (2)}{1006}

2 = f (2.1006)

f (2012) = 2