The range of f(x)= [x], for - 2 <x< 2 is: - Vidyadip

MCQ

The range of $\text{f(x)}=\cos[\text{x}],$ for $-\frac{\pi}{2}<\text{x}<\frac{\pi}{2}$ is:

A
$\{-1,1,0\}$
✓
$\{\cos1,\cos2,1\}$
C
{$\cos1,-\cos1,1$}
D
$[-1,1]$

✓

Answer

Correct option: B.

$\{\cos1,\cos2,1\}$

Since, $\text{f(x)}=\cos[\text{x}],$ where $\frac{-\pi}{2}<\text{x}<\frac{\pi}{2}$
$-\frac{\pi}{2}<\text{x}<\frac{\pi}{2}$
$\Rightarrow-1.57<\text{x}<1.57$
$\Rightarrow[\text{x}]\ \in\ \{-1,0,1,2\}$
Thus, $\cos[\text{x}]=\{\cos(-1),\cos0,\cos1,\cos2\}$
Range of $\text{f(x)}=\{\cos1,1,\cos2\}$

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 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If $\frac{1^3+2^3+3^3+\ldots \ldots \text {.upto } n \text { terms }}{1 \cdot 3+2 \cdot 5+3 \cdot 7+\ldots \ldots \text { upto } n \text { terms }}=\frac{9}{5}$, then the value of $n$ is

Let the co-ordinates of the two points $A\, \& \,B$ be $(1, 2)$ and $(7, 5)$ respectively. The line $AB$ is rotated through $45^o$ in anti clockwise direction about the point of trisection of $AB$ which is nearer to $B$. The equation of the line in new position is :

If $\alpha $ and $\beta $ be the roots of the equation $x^2 - 2x + 2 = 0$ , then the least value of $n$ for ${\left( {\frac{\alpha }{\beta }} \right)^n} = 1$ is

A bag contains $4$ white and $3$ red balls. Two draws of one ball each are made without replacement. Then the probability that both the balls are red is

The tangent$(s)$ from the point of intersection of the lines $2x -3y + 1$ = $0$ and $3x -2y -1$ = $0$ to circle $x^2 + y^2 + 2x -4y$ = $0$ will be -

The base of an equilateral triangle is along the line given by $3x + 4y\,= 9$. If a vertex of the triangle is $(1, 2)$, then the length of a side of the triangle is

For which value of $x$ ; $cosx > sinx,$ where $x\, \in \,\,\left( {\frac{\pi }{2}\,,\,\frac{{3\pi }}{2}} \right)$

The value of a for which the sum of the squares of the roots of the equation $x^2- (a - 2)x - a - 1 = 0$ the least value is:

$\text{XOZ}$ plane divides the join of $(2, 3, 1)$ and $(6, 7, 1)$ in the ratio:

Seven of the eight numbers in a distribution are $11, 16,6, 10, 13, 11, 13.$
Given that the mean of the distribution is $12,$ if $12$ will be included then find the new mean of the distribution.