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

0 < x \leq 1

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0 \leq x \leq 1

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- \infty < x \leq 0

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- \infty < x < 1

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Solution

The correct option is D $- \infty < x < 1$
$2^{x} + 2^{y} = 2 2^{y} = 2 - 2^{x} ∵ 2^{y} > 0 [e x p o n e n t i a l f u n c t i o n] ∴ 2 - 2^{x} > 0 2^{x} < 2 x < 1 ∴ x ϵ (- \infty, 1)$

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