Question

fie f:R->R, f(x) =2x+2013 demonstrați ca f(u) - f(5) supra u-5 aparține Lui N, pt orice u aparține lui R, u diferit de 5​

Answer 1

$f:\mathbb{R}\to \mathbb{R},\quad f(x) = 2x+2013\\ \\\\ \dfrac{f(u)-f(5)}{u-5} = \dfrac{2u+2013 - (2\cdot 5+2013)}{u-5} = \\ \\ =\dfrac{2u+2013 - 2023}{u-5}= \dfrac{2u-10}{u-5} =\dfrac{2(u-5)}{u-5} =\\ \\= 2 \in \mathbb{N},\quad \forall\,u\neq 5$