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Function's Fun f(x^2−2016x)=f(x)⋅x+2016

taitu

New member
Mar 26, 2020
2
f(x^2*2016x) = f(x)x+2016
Then f(2017) = ?
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
Isn't "x^2*2016x" the same as "2016x^3"?
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
617
North Texas

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
Thanks, skeeter. That sounds more reasonable.

f(x^2- 2016x)= f(2017) if x^2- 2016x= 2017. That is the same as x^2- 2016x- 2017= (x+ 1)(x- 2017)= 0 so either x= -1 or x= 2017.

So either f(2017)= -1(f(-1))+ 2016 or f(2017)= 2017 f(2017)+ 2016.

For the latter, -2016= 2016 f(2017) so f(2017)= -1.