SOLUTION: 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).

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 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).      Log On


   

Question 1149406: 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).
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x-f%28y%29%5E%22%22%29+=+f%28x%29-x%2Af%28y%29, f%280%29=3

let x=2016 and y=0

f%282016-f%280%29%5E%22%22%29+=+f%282016%29-2016%2Af%280%29

f%282016-3%29+=+f%282016%29-2016%2A3

f%282013%29+=+f%282016%29-6048

6048+=+f%282016%29-f%282013%29

Answer = 6948

Edwin