The domain of definition of the function f(x) is given by the equation 2x+2y=2 is [2000]

Question

The domain of definition of the function $f (x)$ is given by the equation $2^{x} + 2^{y} = 2$ is [2000]

Smart Achievers · Accepted Answer

(4)

$Given: 2^{x} + 2^{y} = 2,$ $\forall x, y \in R$

$but$ $2^{x}, 2^{y} > 0,$ $\forall x, y \in R$

$∴$ $2^{x} = 2 - 2^{y} < 2$ $\Rightarrow 0 < 2^{x} < 2$ $\Rightarrow x < 1$

$∴$ $Domain = (- \infty, 1)$

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