The domain of the function $y=f(x)$, where $x$ and $y$ are related by $2^x+2^y=2$ is
The domain of the function $y=f(x)$, where $x$ and $y$ are related by $2^x+2^y=2$ is
- $(-\infty, \infty)$
- $(-\infty, 1)$
- $(-1, \infty)$
- $(1, \infty)$
Solution
Given that $2^x+2^y=2 \Rightarrow 2^y=2-2^x$
$
\begin{aligned}
& \because 2^y>0 \Rightarrow 2-2^x>0 \\
& \Rightarrow 2^x < 2 \Rightarrow x < 1 \Rightarrow x \in(-\infty, 1)
\end{aligned}
$
Asked in: AP EAMCET 2023 (19 May Shift 1)
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