Download App

Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
The domain of the function $\cos ^{-1}(2 x-1)$ is
  • ✓
    $[0,1]$
  • B
    $[-1,1]$
  • C
    $(-1,1)$
  • D
    $[0, \pi]$
✓

Answer

Correct option: A.
$[0,1]$
(a) : We know, $0 \leq \cos ^{-1}(2 x-1) \leq \pi$
$\Rightarrow-1 \leq 2 x-1 \leq 1 \Rightarrow 0 \leq 2 x \leq 2 \Rightarrow 0 \leq x \leq 1$
$\therefore$ Domain of $\cos ^{-1}(2 x-1)=[0,1]$

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 Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $I =\frac{2}{\pi} \int_{-\pi / 4}^{\pi / 4} \frac{ dx }{\left(1+ e ^{\sin x}\right)(2-\cos 2 x )}$ then $27 I ^2$ equals. . . . . . . .
→
The maximum value of $f = 4x + 3y$ subject to constraints $\text{x}\geq0,$ $\text{y}\geq0, 2\text{x}+3\text{y}\leq18;\text{x}+\text{y}\geq10$ is:
→
The symbol dx represents:
→
If $a, b, c$ be positive real numbers and the value of $\theta = {\tan ^{ - 1}}\sqrt {\frac{{a(a + b + c)}}{{bc}}} + {\tan ^{ - 1}}\sqrt {\frac{{b(a + b + c)}}{{ca}}} + {\tan ^{ - 1}}\sqrt {\frac{{c(a + b + c)}}{{ab}}} $,then $\tan \theta $ is equal to
→
The radius of a cylinder is increasing at the rate of  $5\ cm/min$, so that its volume is constant. When its radius is $5\ cm$ and height is $3\ cm$,  then the rate of decreases of its height is .......... $cm/min$.
→
If A and B are non - zero square matrices of the same order such that AB = 0, then
→
If $A = \left[ {\begin{array}{*{20}{c}}i&0\\0&i\end{array}} \right]$, then ${A^2} = $
→
$ABCDE$  is a pentagon. Forces $\overrightarrow {AB} ,\,\overrightarrow {AE} ,\,\overrightarrow {DC} ,\,\overrightarrow {ED} $ act at a point. Which force should be added to this system to make the resultant $ 2 \overrightarrow  {AC} $
→
Choose the correct answer from the given four option.
The general solution of $\text{e}^{\text{x}}\cos\text{ydx}-\text{e}^\text{x}\sin\text{ydy}=0$ is:
→
Let a solution $y=y(x)$ of the differential equation $x \sqrt{x^2-1} d y-y \sqrt{y^2-1} d x=0 \quad$ satisfy $y(2)=\frac{2}{\sqrt{3}}$.

$STATEMENT-1$: $y(x)=\sec \left(\sec ^{-1} x-\frac{\pi}{6}\right)$ and

$STATEMENT-2$ : $\mathrm{y}(\mathrm{x})$ is given by $\frac{1}{\mathrm{y}}=\frac{2 \sqrt{3}}{\mathrm{x}}-\sqrt{1-\frac{1}{\mathrm{x}^2}}$

→