Question

Find the domains of definition of the following functions.
$y=\sqrt{2^x-3^x}$

Answer 1

The function

$y=\sqrt{2^x-3^x}$ is defined when

$2^x-3^x\ge 0$

$⟹2^x\ge 3^x$

$⟹x\le 0$

Hence domain is $(-\infty ,0]$