Question

Calculati
[x-1/2]=x-2
[5x-1/3]=2x-1
[4x+3/2]=2x+1
[6x-1/3]=x+6
[3x+4/5]=4x+3/5

Answer 1

[tex][\frac{x-1}{2}]=x-2\\ Egalam\ cu\ k:\\ {[\frac{x-1}{2}]=k(k\ apartine\ lui Z)=\ \textgreater \ x-2=k=\ \textgreater \ x=k+2} \\ {[\frac{x-1}{2}] \leq \frac{x-1}{2}\ \textless \ [\frac{x-1}{2}]+1}\\ k \leq \frac{k+2-1}{2} \ \textless \ k+1 \\ 2k \leq k+1 \ \textless \ 2k+2 \\ 0 \leq -k+1 \ \textless \ 2 \\ -1 \leq -k \ \textless \ 1 \\ 1 \geq k \ \textgreater \ -1 \\ K\ apartine\ {1,0}=\ \textgreater \ x\ apartine\ {3,2}[/tex]