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

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Aicharya · Accepted Answer

$\begin{aligned} & 2^x+2^y=2 \ & \Rightarrow 2^y=2-2^x \ & \Rightarrow y=\log _2\left(2-2^xight) 	ext { is defined, if } 2-2^x\gt0 \ & \Rightarrow 2^x \lt 2 \ & \Rightarrow 2^{x-1} \lt 1 \ & \Rightarrow x-1 \lt 0 \ & \Rightarrow-\infty \lt x \lt 1\end{aligned}$

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

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