Question

If $f:(3,6)\to (1,3)$ is a function defined by $f\left(x\right)=x-\left[\frac{x}{3}\right]$ $($ where $[.]$ denotes the greatest integer function $),$ then $f^{-1}\left(x\right)=$

• A. $x-1$
• B. $x+1$
• C. $x$
• D. none of these

Answer 1

Answer: (B)

$x+1$

Given that $f\left(x\right)=x-\left[\frac{x}{3}\right]$

where $f:(3,6)\to (1,3)$

Now, inside the given domain, we will always have $\left[\frac{x}{3}\right]=1$

$\therefore f\left(x\right)=x-1$ throughout its domain

$\Rightarrow y=x-1$

$\Rightarrow x=y+1=f^{-1}\left(y\right)$

$\therefore f^{-1}\left(x\right)=x+1$