Question

Se considera functie f:R cu valori in R,f(x)=-2x+3.Aratati ca,pentru oricare doua numere intregi a si b , f(a)-f(b)totul supra 2 apartine Z

Answer 1

f(x) =-2x+3

f(a)=-2a+3

f(b)=-2b+3

f(a) - f(b) = -2a+3-(-2b +3) =-2a+3+2b-3 =2b-2a

$\dfrac{f(a)-f(b)}{2}= \dfrac{2b-2a}{2}=\dfrac{2(b-a)}{2}=b-a \in \mathbb{Z}$