The domain of the function ^ -1 (2 x-1) is - Vidyadip

MCQ

The domain of the function $\cos ^{-1}(2 x-1)$ is

A
$[0, \pi]$
B
$[-1,1]$
✓
$[0,1]$
D
$(-1,0)$

✓

Answer

Correct option: C.

$[0,1]$

We have $f(x)=\cos ^{-1}(2 x-1)$
Since, $-1 \leq 2 x-1 \leq 1$
$\Rightarrow 0 \leq 2 x \leq 2$
$\Rightarrow 0 \leq x \leq 1$
$\therefore x \in[0,1]$

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 Model Paper 4→Model Paper 4 — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If the volume of a spherical balloon is increasing at the rate of $ 900$ $cm^3$ $per\, sec$ , then the rate of change of radius of balloon at instant when radius is $ 15\,cm$ [ in $cm/sec$ ]

Which one of the following best represent the graph of $y = \frac{|x-x^2|}{x^2-x}$ ?

The area of the region $\{(\text{x},\text{y}):\text{x}^2+\text{y}^2\leq1\leq\text{x}+\text{y}\}$ is :

If the curve, $y = y ( x )$ represented by the solution of the differential equation $\left(2 x y^{2}-y\right) d x+x d y=0,$ passes through the intersection of the lines, $2 x -3 y =1$ and $3 x+2 y=8,$ then $|y(1)|$ is equal to ...... .

The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) 2 = 3x^2+ 36x + 5.$ The marginal revenue, when $x = 15$ is:

Minimise $\text{Z}=\sum\limits^{\text{n}}_{\text{j}=1}\sum\limits^{\text{m}}_{\text{i}=1}\text{c}_{\text{ij}}\cdot\text{x}_{\text{ij}}$ Subject to $\sum\limits^{\text{m}}_{\text{i}=1}\text{x}_{\text{ji}}=\text{b}_{\text{j}},\text{j}=1,2,....\text{n}$ $\sum\limits^{\text{n}}_{\text{j}=1}\text{x}_{\text{ji}}=\text{b}_{\text{j}},\text{j}=1,2,.....,\text{m}$ is a $\text{LPP}$ with number of constraints.

A coin is tossed $4$ times. The probability that at least one head turns up is:

If $\text{A}=\displaystyle \begin{vmatrix} 2 &\text{amp;}-3 \\ 3 &\text{amp; 2} \end{vmatrix}$ and $\text{B}=\displaystyle \begin{vmatrix} 3 &\text{amp;}-2 \\ 2 &\text{amp; 3} \end{vmatrix}$ then $2\text{ A-B}=$

If the equation of a line $A B$ is $\frac{x-3}{1}=\frac{y+2}{-2}$ $=\frac{z-5}{4}$, find the direction ratios of a line parallel to $A B$.

The minimum number of elements that must be added to the relation $R =\{( a , b ),( b , c )$, (b, d) $\}$ on the set $\{a, b, c, d\}$ so that it is an equivalence relation, is $.........$