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If the Function F : R → R Be Such that F ( X ) = X − [ X ] Where [X] Denotes the Greatest Integer Less than Or Equal to X, Then F − 1 ( X ) (A) 1 X − [ X ] (B) [X] − X (C) Not Defined (D) - Mathematics

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प्रश्न

If the function

\[f : R \to R\]  be such that

\[f\left( x \right) = x - \left[ x \right]\] where [x] denotes the greatest integer less than or equal to x, then \[f^{- 1} \left( x \right)\]

 

विकल्प

  •  \[\frac{1}{x - \left[ x \right]}\]

  • [x] − x

  • not defined

  • none of these

MCQ

उत्तर

f (x) = x - [x]
We know that the range of f is [0, 1).
Co-domain of f = R
As range of f
\[\neq\] Co-domain of f,  f is not onto.
\[\Rightarrow\] f is not a bijective function.
So,  f -1 does not exist.
Thus, the answer is (c).
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अध्याय 2: Functions - Exercise 2.6 [पृष्ठ ७८]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 2 Functions
Exercise 2.6 | Q 37 | पृष्ठ ७८

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