Download App

STD 12 - 1. relation and function — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 1. relation and function1 Mark
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

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

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 1. relation and function→STD 12 - 1. relation and function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $\tan^{-1}(\cot\theta)=2\theta,$ then $\theta=$
→
$A$  and $B$  are two points. The position vector of A is $6b - 2a.$ $A $ point $P $ divides the line $AB$  in the ratio $ 1 : 2.$  If $a - b$ is the position vector of $ P,$  then the position vector of $B $ is given by
→
If $x = x ( y )$ is the solution of the differential equation $y \frac{d x}{d y}=2 x+y^{3}(y+1) e^{y}, x(1)=0$; then $x(e)$ is equal to
→
The values of the constants a, b and for which the function $\text{f(x)}=\begin{cases}(1+\text{ax})^{\frac{1}{\text{x}}},&\text{x}>0\\\text{b},&\text{x}=0\\\frac{(\text{x}+\text{c})^{\frac{1}{2}}-1}{(\text{x}+1)^{\frac{1}{2}}-1},&\text{x}>0\end{cases}$ may be continuous at x = 0, are:
→
The system of linear equations $\lambda x+2 y+2 z=5$ ; $2 \lambda x+3 y+5 z=8$ ; $4 x+\lambda y+6 z=10$ has
→
${(r\,.\,i)^2} + {(r\,.\,j)^2} + {(r\,.\,k)^2} = $
→
Let $f(x) = e^x - e^{-x} + cosx$, then $f(x)$ is 
→
$4tan^{-1} \frac{1}{5} -tan^{-1} \frac{1}{239}$ is equal to
→
The acute angle between the planes $2x - y + z = 0$ and $x + y + 2z = 3$ is:
→
If $\int_{}^{} {\ln ({x^2} + x)dx = x\ln ({x^2} + x) + A} $, then $A = $
→