The domain of ^ - 1 [ _3 ( x 3 ) ] is - Vidyadip

MCQ

The domain of ${\sin ^{ - 1}}\left[ {{{\log }_3}\left( {\frac{x}{3}} \right)} \right]$ is

✓
$[1, 9]$
B
$[-1, 9]$
C
$[-9, 1]$
D
$[-9, -1]$

✓

Answer

Correct option: A.

$[1, 9]$

a
(a) $y = {\sin ^{ - 1}}\left[ {{{\log }_3}\left( {\frac{x}{3}} \right)} \right]$

==> $ - 1 \le {\log _3}\left( {\frac{x}{3}} \right) \le 1$

==> $\frac{1}{3} \le \frac{x}{3} \le 3$ ==> $1 \le x \le 9$ ==> $x \in [1,\,9]$.

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 STD 12 - 1. relation and function→STD 12 - 1. relation and function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\int {\frac{{1 + x + \sqrt {x + {x^2}} }}{{\sqrt x \, + \sqrt {1 + x} }}\,\,dx = } $

The solution of differential equation $x\frac{{dy}}{{dx}} + y = {y^2}$ is

$\Delta = \left| {\,\begin{array}{*{20}{c}}{a + x}&b&c\\b&{x + c}&a\\c&a&{x + b}\end{array}\,} \right|$,which of the following is a factor for the above determinant

If $\vec a = 2\hat i - \hat j + \hat k,\,\,\vec b = \hat i + \hat j - 2\hat k$ and $\vec c = \hat i + 3\hat j - \left( {{\lambda ^2} + 3\lambda } \right)\hat k$ (where $\lambda $ is a constant) and $\vec a $ is perpendicular to $\vec c - \lambda \vec b$, then sum of different values of $\lambda$ is

If $\int\limits_1^2 {\frac{{dx}}{{{{\left( {{x^2} - 2x + 4} \right)}^{\frac{3}{2}}}}} = \frac{k}{{k + 5}}} $ then $k$ is equal to

$\int {\frac{{2x + 5}}{{\sqrt {7 - 6x - {x^2}} }}dx} = A\sqrt {7 - 6x - {x^2}} + B\,{\sin ^{ - 1}}\left( {\frac{{x + 3}}{4}} \right) + C$ (where $C$ is a constant of integration), then the ordered pair $(A, B)$ is equal to

If $f ‘ (x) =$ $\left| {\begin{array}{*{20}{c}}{mx}&{mx - p}&{mx + p}\\n&{n + p}&{n - p}\\{mx + 2n}&{mx + 2n + p}&{mx + 2n - p}\end{array}} \right|$ then $y = f(x)$ represents

$ \begin{bmatrix}1 & \text{x} & \text{x}^2 \\1 & \text{y} & \text{y}^2 \\1 & \text{z} & \text{z}^2\end{bmatrix}$

Let $X$ be a family of sets and $R$ be a relation on $X$ defined by $‘A$ is disjoint from $B’$. Then $R$ is

If $A$ and $B$ are two events such that $\text{P}(\text{A}|\text{B})=\text{p},\text{P(A)}=\text{p},\text{P(B)}=\frac{1}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then $p =$