The domain of the function $f(x) = \frac{1}{\sqrt{|x|-x}}$ is
- A$(0, \infty)$
- B$(-\infty, 0)$
- C$(-\infty, \infty) \setminus \{0\}$
- D$(-\infty, \infty)$
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Similar Questions
If the domain of the function $f(x) = \sqrt{\ln(m\sin x + 4)}$ is $R$,then the number of possible integral values of $m$ is:
Consider the following lists.
$A$. $f(x)=\frac{|x+2|}{x+2}, x \neq-2$ $1$. $[\frac{1}{3}, 1]$ $B$. $g(x)=|[x]|, x \in R$ $2$. $Z$ $C$. $h(x)=|x-[x]|, x \in R$ $3$. $W$ $D$. $f(x)=\frac{1}{2-\sin 3x}, x \in R$ $4$. $[0, 1)$ $5$. $\{-1, 1\}$
| $A$. $f(x)=\frac{|x+2|}{x+2}, x \neq-2$ | $1$. $[\frac{1}{3}, 1]$ |
| $B$. $g(x)=|[x]|, x \in R$ | $2$. $Z$ |
| $C$. $h(x)=|x-[x]|, x \in R$ | $3$. $W$ |
| $D$. $f(x)=\frac{1}{2-\sin 3x}, x \in R$ | $4$. $[0, 1)$ |
| $5$. $\{-1, 1\}$ |
Match the following functions with their respective ranges:
Function Range $A. f(x) = |x|$ $I. [0, \infty)$ $B. f(x) = x^2$ $II. \mathbb{R}$ $C. f(x) = x^3$ $III. [0, \infty)$ $D. f(x) = \text{sgn}(x)$ $IV. \{-1, 0, 1\}$
| Function | Range |
|---|---|
| $A. f(x) = |x|$ | $I. [0, \infty)$ |
| $B. f(x) = x^2$ | $II. \mathbb{R}$ |
| $C. f(x) = x^3$ | $III. [0, \infty)$ |
| $D. f(x) = \text{sgn}(x)$ | $IV. \{-1, 0, 1\}$ |
The domain of the function $f(x) = \exp (\sqrt {5x - 3 - 2{x^2}} )$ is
Easy
View SolutionThe range of the function $f(x) = \sqrt{3-x} + \sqrt{2+x}$ is
DifficultJEE MAIN 2023
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