• # question_answer If $f:R\to R$is defined by $f(x)=[2x]-2[x]$ for all $x\in R,$where $[x]$is the greatest integer not exceeding x, then the range of$f$is A) $\{x\in R:0\le x\le 1\}$ B)  $(0,1)$ C)  $\{x\in R:x>0\}$ D)  $\{x\in R:x\le 0\}$

Given, $f(x)=[2x]-2[x],\forall \,x\in R$ Let $x$is an integer, then $f(x)=0$ and let $x$is not an integer, then $f(x)=1$ $\therefore$ Range of $f(x)=\{0,1\}$