If f: R rightarrow R is defined by f(x) = [fr | vedclass

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(D) Given,$f(x) = [\frac{x}{5}]$ where $|x| < 71$. This implies $-71 < x < 71$. Dividing by $5$,we get $-\frac{71}{5} < \frac{x}{5} < \frac{71}{5}$. $

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$\{-15, -14, \ldots, 0, \ldots, 13, 14\}$

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(D) Given,$f(x) = [\frac{x}{5}]$ where $|x| This implies $-71 Dividing by $5$,we get $-\frac{71}{5} $-14.2 Now,we find the range of the greatest integer function $[\frac{x}{5}]$. The minimum value is $[\frac{x}{5}] = [-14.2] = -15$. The maximum value is $[\frac{x}{5}] = [14.2] = 14$. Since $x$ can take any real value in the interval $(-71, 71)$,the function $f(x)$ will take all integer values from $-15$ to $14$. Thus,the set is $\{-15, -14, \ldots, 0, \ldots, 13, 14\}$.

If $f: R \rightarrow R$ is defined by $f(x) = [\frac{x}{5}]$ for $x \in R$,where $[y]$ denotes the greatest integer not exceeding $y$,then $\{f(x) : |x| < 71\}$ is equal to

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