The domain of the function f(x) = ^ - 1 [ _2 (x/2)] is - Vidyadip

MCQ

The domain of the function $f(x) = {\sin ^{ - 1}}[{\log _2}(x/2)]$ is

✓
$[1, 4]$
B
$[-4, 1]$
C
$[-1, 4]$
D
None of these

✓

Answer

Correct option: A.

$[1, 4]$

a
(a) $f(x) = {\sin ^{ - 1}}[{\log _2}(x/2)]$, Domain of ${\sin ^{ - 1}}x$ is $x \in [ - 1,\,1]$

==> $ - 1 \le {\log _2}(x/2) \le 1$ ==> $\frac{1}{2} \le \frac{x}{2} \le 2$

==> $1 \le x \le 4$

$\therefore$ $x \in [1,\,4]$.

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 1. relation and function→1. relation and function — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\smallint \frac{{{{\sin }^2}x{{\cos }^2}x}}{{{{\left( {{{\sin }^5}x + {{\cos }^3}x{{\sin }^2}x + {{\sin }^3}x{{\cos }^2}x + {{\cos }^5}x} \right)}^2}}}dx$

$\cot ^{-1} \frac{\sqrt{1-x^2}}{x}$ equal to :

The general solution of the differential equation, $x \left( {\frac{{dy}}{{dx}}} \right) = y \cdot \ln \left( {\frac{y}{x}} \right)$ is :
where $c$ is an arbitrary constant.

The relation $R$ defined on the set $A = \{1, 2, 3, 4, 5\}$ by $R = \{(x, y)$ : $|{x^2} - {y^2}| < 16\} $ is given by

The probability distribution of $X$ is

$X=x$	0	1	2	3	4
$P(X=x)$	$k$	$2k$	$4k$	$2k$	$k$

Then find $P(X \leq 1)$.

There are two value of a which makes the determinant $\triangle=\begin{vmatrix}1&-2&5\\2&\text{a}&-1\\0&4&2\text{a}\end{vmatrix}$ equal to 86. The sum of these two values is:

4
5
-4
9

The minimum value of $2{x^2} + x - 1$ is

The number of equivalence relations in the set $\{1,2,3\}$ containing the elements $(1,2)$ and $(2,1)$ is

If $\text{f}(\text{x})=(\cos\text{x}+\text{i}\sin\text{x})(\cos2\text{x}+\text{i}\sin2\text{x})(\cos3\text{x}+\text{i}\sin3\text{x})...(\cos\text{nx}+\text{i}\sin\text{nx})\ \text{and}\ \text{f}(1)=1, $ then f1 is equals to:

$$$\frac{\text{n}(\text{n}+1)}{2}$
$\Big\{\frac{\text{n}(\text{n}+1)}{2}\Big\}^2$
$-\Big\{\frac{\text{n}(\text{n}+1)}{2}\Big\}^2$
$\text{none of these}$

Let $f:R \to R$ be a function defined by $f(x) = \max \,(x,\,{x^3}).$ The set of all points where $f(x)$ is not differentiable is