Question

fie functia f:R-R, f(x)=2x+1. Sa se demonstreze ca f(k)+f(k+3)=f(k+1)+f?(k+2) oricare k apartine lui R

Answer 1

f(k)=2k+1
f(k+3)=2(k+3)+1=2k+7
f(k)+f(k+3)=2k+1+2k+7=4k+8 (1)
f(k+1)=2(k+1)+1=2k+3
f(k+2)=2(k+2)+1=2k+5
f(k+1)+f(k+2)=2k+3+2k+5=4k+8 (2)
Din (1) si (2) rezulta ca f(k)+f(k+3)=f(k+1)+f(k+2)