If domain of function f(x) = √ {ln left( {msin x + 4} right)} is R , then number of po

English

Gujarati

Hindi

1.Relation and Function

normal

If domain of function $f(x) = \sqrt {\ln \left( {m\sin x + 4} \right)} $ is $R$ , then number of possible integral values of $m$ is

A

$3$

B

$4$

C

$6$

D

$7$

Solution

$ln(m\sin x + 4) \ge 0 \Rightarrow m\sin x + 4 \ge 1$

$m \sin x \geq-3 \Rightarrow m \in[-3,3]$

$7$ possible integral values.

Standard 12

Mathematics

Share

Similar Questions

The domain of ${\sin ^{ – 1}}({\log _3}x)$ is

easy

Let $f : R -\{0,1\} \rightarrow R$ be a function such that $f(x)+f\left(\frac{1}{1-x}\right)=1+x$. Then $f(2)$ is equal to :

hard

(JEE MAIN-2023)

Range of the function $f(x) = {\sin ^2}({x^4}) + {\cos ^2}({x^4})$ is

normal

If $f$ is an even function defined on the interval $(-5, 5),$ then four real values of $x$ satisfying the equation $f(x) = f\left( {\frac{{x + 1}}{{x + 2}}} \right)$ are

hard

(IIT-1996)

Let $\quad E_1=\left\{x \in R : x \neq 1\right.$ and $\left.\frac{x}{x-1}>0\right\}$ and $\quad E_2=\left\{x \in E_1: \sin ^{-1}\left(\log _e\left(\frac{x}{x-1}\right)\right)\right.$ is a real number $\}$.

(Here, the inverse trigonometric function $\sin ^{-1} x$ assumes values in $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ )

Let $f : E _1 \rightarrow R$ be the function defined by $f(x)=\log _c\left(\frac{x}{x-1}\right)$ and $g: E_2 \rightarrow R$ be the function defined by $g(x)=\sin ^{-1}\left(\log _e\left(\frac{x}{x-1}\right)\right)$

$LIST I$ $LIST II$

$P$ The range of $f$ is $1$ $\left(-\infty, \frac{1}{1- e }\right] \cup\left[\frac{ e }{ e -1}, \infty\right)$

$Q$ The range of $g$ contains $2$ $(0,1)$

$R$ The domain of $f$ contains $3$ $\left[-\frac{1}{2}, \frac{1}{2}\right]$

$S$ The domain of $g$ is $4$ $(-\infty, 0) \cup(0, \infty)$

$5$ $\left(-\infty, \frac{ e }{ e -1}\right]$

$6$ $(-\infty, 0) \cup\left(\frac{1}{2}, \frac{ e }{ e -1}\right]$

The correct option is:

medium

(IIT-2018)