If the function f : R R be such that f(x) = x - [x], where [x] de… - Vidyadip

MCQ

If the function $f : R \rightarrow R$ be such that $f(x) = x - [x],$ where $[x]$ denotes the greatest integer less than or equal to $x,$ then $f^{-1}(x)$ is:

A
$\frac{1}{\text{x}-[\text{x}]}$
B
$[x] - x$
✓
Not defined
D
None of these.

✓

Answer

Correct option: C.

Not defined

Given function is $f(x) = x - [x]$
$[x]$ is a greatest integer function.
Hence, we will have same values of the function for the different values of $x.$
As we are considering integer only not fraction part.
Hence, it is not defined.

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 RELATIONS AND FUNCTIONS→RELATIONS AND FUNCTIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of $\int_0^{{{\sin }^2}x} {{{\sin }^{ - 1}}\sqrt t \,dt + \int_0^{{{\cos }^2}x} {{{\cos }^{ - 1}}\sqrt t \,dt} } $ is

The function $\text{f(x)}=\begin{cases}\frac{\text{x}^2}{\text{a}},&0\leq\text{x}<1\\\text{a},&1\leq\text{x}<\sqrt{2}\\\frac{2\text{b}^2-4\text{b}}{\text{x}^2},&\sqrt{2}\leq\text{x}<\infty\end{cases}$ is continuous for $0\leq\text{x}<\infty,$ then the most suitable values of a and b are:

Let $g(x) = | |x + 2| -3|$ . If $'a'$ denotes the number of relative minima, $'b'$ denotes the number of relative maxima and $'c'$ denotes the product of the zeroes of $g(x)$ , then the value of $(a + 2b -c)$ is

Product of all the solution of the equation ${x^{1 + {{\log }_{10}}x}} = 100000x$ is

If the minimum value of an objective function $Z=a x+$ by occurs at two points $(3,4)$ and $(4,3)$ then

The integral $\int {\frac{{3{x^{13}}\, + \,\,2{x^{11}}}}{{{{(2{x^4}\, + \,3{x^2}\, + \,1)}^4}}}dx} $ is equal to (where $C$ is a constant of integration)

Let $f(x) = [2x^3 -5];$ then number of points in $(1, 2)$ where the function is discontinuous are where $[\,.]\, \to G.I.F$

If $A=\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}4 & 0 \\ -1 & 1\end{array}\right]$, then value of $x$ for which $A^2=B$ is

If $\vec{a},\vec{b},\vec{c}$ are non-coplanar vectors and $(\vec{a} - \lambda \vec{b}) . (\vec{b} - 2\vec{c}) \times (\vec{c} + 2 \vec{a}) =0$ ,then $\lambda$ is equal to

The number of points, where the curve $f(x)=e^{8 x}-e^{6 x}-3 e^{4 x}-e^{2 x}+1, x \in R$ cuts $x$-axis, is equal to