The domain of definition of the function $f(x)$ given by the equation $2^x + 2^y = 2$ is
- A$0 < x \leqslant 1$
- B$0 \leqslant x \leqslant 1$
- C$-\infty < x \leqslant 0$
- D$-\infty < x < 1$
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Similar Questions
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 $f(x) = [\log_{10}(\frac{5x - x^2}{4})]^{1/2}$ is
Medium
View SolutionLet $A = \{x \in R, x \neq 0, -4 \leq x \leq 4\}$ and $f: A \rightarrow R$ be defined by $f(x) = \frac{|x|}{x}$ for $x \in A$. Then, the range of $f$ is
The range of the function $f(x) = \log_{\sqrt{5}}(3 + \cos(\frac{3\pi}{4} + x) + \cos(\frac{\pi}{4} + x) + \cos(\frac{\pi}{4} - x) - \cos(\frac{3\pi}{4} - x))$ is:
DifficultJEE MAIN 2021
View SolutionThe range of the function $f(x) = \sqrt{9 - x^2}$ is
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