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Composite Function

Let fx=x-[x...

Question

Let $f (x) = x - [x]$ then $f^{'} (x) = 1$ for what values of $x$
(Note : $[x]$ denotes the greatest integer less than or equal to $x$ )

x \in R

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x \in R - {0}

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x \in R - Z

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x \in R - {1}

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Solution

The correct option is C $x \in R - Z$
$f (x) = x - [x] = {\begin{matrix} 0 x \in z x - c x \notin z \end{matrix} ∴ f^{'} (x) = {\begin{matrix} D N E x \in z 1 x \notin z \end{matrix}$
Where $D N E$ means does not exits

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