Let `f:(4,6)vec(6,8)` be a function defined by `f(x)=x+[x/2]dotw h e r e[dot]` denotes the greatest integer function, then `f^(-1)(x)` is equal to (A) `x-2` (B) `x-[x//2]` (C) `-x-2` (D) none of these

Options

A. `x - [ (x)/(2)]`
B. `- x - 2 `
C. `x - 2 `
D. `(1)/(x + [(x)/(2)]) `

Answer

C

Explanation

We have, `f'(4,6) to (6,8)` such that
`f (x) = x+ [(x)/(2)]=2`
For `x in (4,6)` we have
`(x)/(2) in (2,3) rArr [(x)/(2)]= 2`
`therefore f(x) = x+2`
Now
`f^(-1) "of" (x) = x`
`rArr f^(-1) (x(x)) = x rArr f^(-1) (x+2) = x rArr f^(-1) (x) = x -2`