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 $x+3$

$f\left(x\right)=x-\left[x\right]f:(3,4)\to (0,1)$

For $x\in (3,4)$

$\left[x\right]=3\Rightarrow f\left(x\right)=x-3y=x-3x=y+3f^{-1}\left(x\right)=x+3$

So option $D$ is correct.