An algebra problem by IR J

Algebra Level 3

Let f be a real-valued function such that $f(x-f(y)) = f(x)-xf(y)$ for any real numbers x and y.

If $f(0) = 3$ , determine $f(2016)-f(2013)$ .

1 solution

Hugh Sir
Nov 21, 2018

$f(x-f(y)) = f(x)-xf(y)$ and $f(0) = 3$

Substituting $x = 2016$ and $y = 0$ yields

$f(2016-f(0)) = f(2016)-(2016 \times f(0))$

$f(2016-3) = f(2016)-(2016 \times 3)$

$f(2013) = f(2016)-6048$

Therefore, $f(2016)-f(2013) = \boxed{6048}$ .