Question

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

• A. $0<x\le 1$
• B. $0\le x\le 1$
• C. $-\infty <x\le 0$
• D. $-\infty <x<1$

Answer 1

Answer: (D)

$2^x+2^y=2$
$2^y=2-2^x$
$y={\log }_2(2-2x)$
$\text{ or }y={\log }_2\left(2-2^x\right)$
$2-2^x>0$
$x<1$