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The inverse of $f(x)=x-[x],$ where $[x]$ is greatest integer function is

$\begin{array}{1 1} (A) \large\frac{1}{x-[x]} \\(B)\; [x]-x \\ (C)\; not \;defined \\(D) none \;of\; these \end{array}$

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  • For inverse of a function to be defined it should be bijective function.
$f(x)=x-n$ when $x \in (n,n+1)$ and $f(x)=0\: when\:x=n$
$\Rightarrow $ $f(x)$ is not 1-1 function but is many to one function.
$\Rightarrow f(x)$ is not bijective function
$\Rightarrow\:f^{-1}(x)$ is not defined.
answered May 2, 2013 by rvidyagovindarajan_1

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