Question

Let $f:(4,6)\to (6,8)$ be a function defined by $f\left(x\right)=x+2$ (where $[.]$ denote the greatest integer function), then $f^{-1}\left(x\right)$ is equal to

• A. $x-\left[\frac{x}{2}\right]$
• B. $-x-2$
• C. $x-2$
• D. $\frac{1}{x+\left[\frac{x}{2}\right]}$

Answer 1

Answer: (C)

$x-2$

Since $f:(4,6)\to (6,8)$

$f\left(x\right)=x+2$

Let $y=x+2\Rightarrow x=y-2$

$f^{-1}\left(y\right)=y-2$

Replacing $x$ by $y$ and $y$ by $x$, we get

$f^{-1}\left(x\right)=x-2$