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STD 12 - 1. relation and function — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 1. relation and function4 Marks
MCQ
Let $f : (4, 6) \to (6,8)$ be a function defined by $f(x) = x + [\frac{x}{2}]$ (where $[.]$ denotes the greatest integer function) , then $f^{-1} (x)$ is euqal to
  • A
    $x- [\frac{x}{2}]$
  • B
    $-x -2$
  • ✓
    $x -2$
  • D
    $\frac{1}{x+[\frac{x}{2}]}$
✓

Answer

Correct option: C.
$x -2$
c
$x \in(4,6)$

$\frac{x}{2} \in(2,3)$

$\left[\frac{x}{2}\right] \in 2$

$\therefore y=x+\left[\frac{x}{2}\right]=x+2$

$y-2=x$

Or

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

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