If the function f: R R be such that f(x) = x - [x], where [x] den… - Vidyadip

MCQ

If the function $f: R \rightarrow R$ be such that $f(x) = x - [x],$ where $[x]$ denotes the greatest integer less than or equal to $x$, then $f^{-2}(x)$ is:

A
$\frac{1}{\text{x}-[\text{x}]}$
B
$[x] - x$
✓
Not defined
D
None of these.

✓

Answer

Correct option: C.

Not defined

Given function is $f(x) = x - [x]$
$[x]$ is a greatest integer function.
Hence, we will have same values of the function for the different values of $x.$
As we are considering integer only not fraction part.
Hence, it is not defined.

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