Question

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

• A. $\frac{1}{x - \lbrack x\rbrack}$
• B. $\lbrack x\rbrack - x$
• C. Not defined
• D. None

Answer 1

Answer: (C)

Not defined

Answer 2

$f(x) = x - \lbrack x\rbrack$ Since, for $x = 0 \Rightarrow f(x) = 0$

For $x = 1 \Rightarrow f(x) = 0$.

For every integer value of $x,f(x) = 0$

$\Rightarrow$ $f(x)$ is not one-one $\Rightarrow$ So $f^{- 1}(x)$ is not defined.