The domain of the definition of the function | vedclass

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(D) Given the equation $2^x + 2^y = 2$. Rearranging for $2^y$,we get $2^y = 2 - 2^x$. Since $2^y > 0$ for all real $y$,the expression $2 - 2^x$ must b

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$-\infty < x < 1$

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(D) Given the equation $2^x + 2^y = 2$. Rearranging for $2^y$,we get $2^y = 2 - 2^x$. Since $2^y > 0$ for all real $y$,the expression $2 - 2^x$ must be strictly greater than $0$. $2 - 2^x > 0 \Rightarrow 2^x Since $2 = 2^1$,we have $2^x Since the base $2 > 1$,the inequality holds for $x Thus,the domain is $(-\infty, 1)$,which is written as $-\infty < x < 1$.

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

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