The domain of ^ -1 (x^2-4 ) is: - Vidyadip

MCQ

The domain of $\cos^{-1}\big(\text{x}^2-4\big)$ is:

A
$[3,5]$
B
$[-1,1]$
✓
$\Big[-\sqrt5,-\sqrt3\Big]\cup\Big[\sqrt3,\sqrt5\Big]$
D
$\Big[-\sqrt5,-\sqrt3\Big]\cap\Big[\sqrt3,\sqrt5\Big]$

✓

Answer

Correct option: C.

$\Big[-\sqrt5,-\sqrt3\Big]\cup\Big[\sqrt3,\sqrt5\Big]$

Let, $\cos^{-1}\big(\text{x}^2-4\big)=\text{y}$
$\Rightarrow\cos\text{y}=\text{x}^2-4$
$\Rightarrow-1\leq\text{x}^2-4\leq1$
$\Rightarrow3\leq\text{x}^2\leq5$
$\Rightarrow\pm\sqrt3\leq\text{x}\pm\sqrt5$
$\text{x}\in\Big[-\sqrt5,-\sqrt3\Big]\cup\Big[\sqrt3,\sqrt5\Big]$

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

Let $f,\ f',\ f''$ be continuous in $[0, ln\ 2]$ and $f(0) = 0 , f '(0) = 3, f(ln\ 2) = 6 , f'(ln\ 2) = 4$ and $\int\limits_0^{\ln 2} {{e^{ - 2x}}f(x)dx} = 3$ , then $\int\limits_0^{\ln 2} {{e^{ - 2x}}f''(x)dx} $ is

If $\angle A = {90^o}$ in the triangle ABC, then ${\tan ^{ - 1}}\left( {\frac{c}{{a + b}}} \right) + {\tan ^{ - 1}}\left( {\frac{b}{{a + c}}} \right) = $

Two dice are thrown. If it is known that the sun of the numbers on the dice was less than 6, than the probability of gettinga sum 3, is

If $u = x{y^2}{\tan ^{ - 1}}\left( {{y \over x}} \right)$, then $x{u_x} + y{u_y} = $

The area of the region bounded by the line $y = | x - 2 |, x = 1, x = 3$ and $x-$axis is:

$\int_0^\pi {\frac{{x\,\tan x}}{{\sec x + \cos x}}} \,dx = $

If ${\tan ^{ - 1}}x - {\tan ^{ - 1}}y = {\tan ^{ - 1}}A,$ then $A$

If $A$ is a square matrix of order $3$ such that the value of $|\operatorname{adj} A|=8$, then the value of $\left|A^{\top}\right|$ is

Evaluate : $\sin \left[\frac{\pi}{3}+\sin ^{-1}\left(\frac{1}{2}\right)\right]$

If the function $\text{f}(\text{x})=\cos|\text{x}|-2\text{ax}+\text{b}$ increases along entire number scale, then: