Question

daca f, g definite pe R , f(x)=2[x] iar g(x)=3x-4 sa se afle x astfel încât f(x)=g(x)

Answer 1

Răspuns:

Explicație pas cu pas:

$2{[x]}=3x-4\\{[x]}=\dfrac{3x-4}{2}\\\dfrac{3x-4}{2}\stackrel{not}{=} k\in\mathbb{Z}\Rightarrow x=\dfrac{2k+4}{3}\\x-1<{[x]}\leqslant x\\\dfrac{2k+4}{3}-1<k\leqslant\dfrac{2k+4}{3}\\\dfrac{2k+1}{3}<k\leqslant \dfrac{2k+4}{3}|\cdot 3\\2k+1<3k\leqslant 2k+4 |-2k\\1<k\leqslant 4\\k\in\mathbb{Z}\Rightarrow k\in\{2,3,4\}\\x=\dfrac{2k+4}{3}\\k=2\Rightarrow x=\dfrac{8}{3}\\k=3\Rightarrow x=\dfrac{10}{3}\\k=4\Rightarrow x=4\\S:x\in\left\{\dfrac{8}{3},\dfrac{10}{3},4\right\}$