The domain of the definition of the function $y(x)$ is given by the equation $2^x+2^y=2$ is

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Aicharya · Accepted Answer

$\begin{aligned} & 2^x+2^y=2 \ & \Rightarrow 2^y=2-2^x \ & \Rightarrow y=\log _2\left(2-2^xight) 	ext { is defined, if } 2-2^x>0 \ & \Rightarrow 2^x < 2 \ & \Rightarrow 2^{x-1} < 1 \ & \Rightarrow x-1 < 0 \ & \Rightarrow-\infty < x < 1\end{aligned}$

The domain of the definition of the function $y(x)$ is given by the equation $2^x+2^y=2$ is

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