Question

104 b , 108 c d pls.​

Answer 1

$\bf 104.\\ \\ \it b)\ B(n)=\dfrac{2n+1}{n}=\dfrac{2n}{n}+\dfrac{1}{n}=2+\dfrac{1}{n} \Rightarrow2 < B(n)\leq 3\\ \\ \\ n=1 \Rightarrow [B(n)]=3\\ \\ n > 1 \Rightarrow [B(n)]=2$

$\bf 108.\\ \\ \it c)\ \ [4x]=3 \Rightarrow 3\leq4x < 4\Big|_{:4} \Rightarrow \dfrac{3}{4}\leq x < 1 \Rightarrow x\in \Big[ \dfrac{3}{4},\ \ 1\Big)$

$\it d)\ \{x\}=\dfrac{3}{4} \Rightarrow \begin{cases}\ x=n+\dfrac{3}{4},\ \forall n\in\mathbb{Z_+}\\ \\ \\ \\ x=n-\dfrac{1}{4},\ \forall n\in \mathbb{Z}_-\end{cases}$