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If-f-R-R-is-a-function-such-that-f-0-1-and-f-x-f-y-f-x-y-for-all-x-y-R-then-A-1-is-a-period-of-f-B-f-n-1-for-all-integers-n-C-f-n-n-for-all-integers-n-D-f-1-0-




Question Number 119801 by Ar Brandon last updated on 27/Oct/20
If f:R→R is a function such that f(0)=1 and f(x+f(y))=  f(x)+y for all x, y∈R, then  (A) 1 is a period of f  (B) f(n)=1 for all integers n  (C) f(n)=n for all integers n  (D) f(−1)=0
Iff:RRisafunctionsuchthatf(0)=1andf(x+f(y))=f(x)+yforallx,yR,then(A)1isaperiodoff(B)f(n)=1forallintegersn(C)f(n)=nforallintegersn(D)f(1)=0

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