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Standard XII

Mathematics

Inverse of a Function

If the functi...

Question

If the function $f : R \to R$ be such that $f (x) = x - [x],$ where $[y]$ denotes the greatest integer less than or equal to $y$ , then $f^{- 1} (x)$ is

\frac{1}{x - [x]}

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[x] - x

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not defined

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none of these

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Solution

The correct option is A not defined
$f (x) = x - [x] = {x}$ is not one-one function from R to R. Hence $f^{- 1} (x)$ can not be defined.

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If the function f:R→R be such that f(x)=x−[x], where [y] denotes the greatest integer less than or equal to y, then f−1(x) is

The correct option is A not definedf(x)=x−[x]={x} is not one-one function from R to R. Hence f−1(x) can not be defined.

If the function $f : R \to R$ be such that $f (x) = x - [x],$ where $[y]$ denotes the greatest integer less than or equal to $y$ , then $f^{- 1} (x)$ is

The correct option is A not defined
$f (x) = x - [x] = {x}$ is not one-one function from R to R. Hence $f^{- 1} (x)$ can not be defined.