Q. Let $f:(2,\ 3) \rightarrow (0,\ 1)$ be defined by $f(x) = x - \lbrack x\rbrack$, then $f^{- 1}(x)$ equals
A) $x - 2$
B) $x + 1$
C) $x - 1$
D) $x + 2$
Explanation
(d)
Given,
$\ \ \ \ \ \ \ \ \ \ f(x) = x - \lbrack x\rbrack$
For $2 < x < 3$, then value of $\lbrack x\rbrack$ is 2
Let $y = f(x) = x - 2,\ 2 < x < 3$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ x = 2 + y$
$\therefore\ \ \ \ f^{- 1}(x) = 2 + x$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.