(B) Given $f(x) = [2x] - 2[x]$.Case $1$: If $x$ is an integer,let $x = n$ where $n \in Z$.Then $f(n) = [2n] - 2[n] = 2n - 2n = 0$.Case $2$: If $x$ is

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(B) Given $f(x) = [2x] - 2[x]$.Case $1$: If $x$ is an integer,let $x = n$ where $n \in Z$.Then $f(n) = [2n] - 2[n] = 2n - 2n = 0$.Case $2$: If $x$ is not an integer,let $x = n + f$ where $n \in Z$ and $0 Then $f(x) = [2(n + f)] - 2[n + f] = [2n + 2f] - 2n = 2n + [2f] - 2n = [2f]$.Since $0 However,for any non-integer $x$,$[2x] - 2[x]$ always evaluates to $1$.Therefore,the range of $f$ is $\{0, 1\}$.

Class 11 Chemistry Data Entry - Chemistry Level 0 of all question bank

If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$,where $[x]$ is the greatest integer function,then the range of $f$ is:

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A
$\{x \in R: 0 \leq x \leq 1\}$
B
$\{0, 1\}$
C
$\{x \in R: x > 0\}$
D
$\{x \in R: x \leq 0\}$

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If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$,where $[x]$ is the greatest integer function,then the range of $f$ is:

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