Question

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

• A. (0, 1]
• B. [0, 1]
• C. $( - \infty,0\rbrack$
• D. $( - \infty,1)$

Answer 1

Answer: (D)

$( - \infty,1)$

Answer 2

$2^{y} = 2 - 2^{x}$

y is real if $2 - 2^{x} \geq 0$ ⇒ $2 > 2^{x}$⇒ $1 > x$

$x \in ( - \infty,1)$