Thank you for reporting, we will resolve it shortly
Q.
Let $f :(2,3) \rightarrow(0,1)$ be defined by $f ( x )= x -[ x ]$. Then, $f ^{-1}( x )$ equals to
Relations and Functions - Part 2
Solution:
The given function is
$f :(2,3) \rightarrow(0,1)$ defined by
$f ( x )= x -[ x ]$
Let $y \in(0,1)$ such that $y = f ( x )$
$\therefore y = x -2$
$\{\because 2 < x < 3 \Rightarrow [ x ]=2\}$
$\Rightarrow x = y + 2 $
$\therefore f^{-1} (y) = y + 2$
$\left[\because x = f ^{-1}( y )\right]$
$\Rightarrow f ^{-1}( x )= x +2$