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If $f: R \rightarrow R$ is defined by $f(x)=[2 x]-2[x]$ for $x \in R$, where $[x]$ is the greatest integer not exceeding $x$, then the range of $f$ is :
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Verified Answer
The correct answer is:
$\{0,1\}$
$\because \quad f(x)=[2 x]-2[x] \forall x \in R$
Let $x$ is an integer, then
$f(x)=0$
and let $x$ is not an integer, then
$quad f(x)=1$
$\therefore$ Range of $f(x)=\{0,1\}$
Let $x$ is an integer, then
$f(x)=0$
and let $x$ is not an integer, then
$quad f(x)=1$
$\therefore$ Range of $f(x)=\{0,1\}$
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