Question

If $f:(3,4)\to (0,1)$ is defined by $f\left(x\right)=x-\left[x\right]$ where $\left[x\right]$denotes the greatest integer function then $f^{-1}\left(x\right)$ is

• A. $\frac{1}{x-\left[x\right]}$
• B. $\left[x\right]-x$
• C. $x-3$
• D. $x+3$

Answer 1

The correct option is D $x+3$

Note that $f\left(x\right)=x-\left[x\right]=\left\{x\right\}$. Hence every number $x\in \left(3,4\right)$ is mapped to its fractional part.
Hence, the inverse of the function can be written by adding the integer part of the number i.e., $3$ to each of the fraction part.
Hence the function $f^{-1}\left(x\right)=x+3$.