Question

The domain of two definition of the function f(x) is 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

The correct option is D $-\infty <x<1$

We have, $2^x+2^y=2$
$\Rightarrow 2^y=2-2^x\Rightarrow y=lo{g}_2(2-2^x)$
$\Rightarrow 2-2^x$ > 0 ($\therefore$ y is real)
$\Rightarrow 2^x<2\Rightarrow 2^{x-1}<1\Rightarrow x-1<0$
$\Rightarrow x<1\Rightarrow -\infty <x<1$