# How do you find the domain of g(t)= sqrt(1-2^t)?

Apr 16, 2015

Assuming we are restricted to Real numbers:

${2}^{t} > 1$ for all $t > 0$

$g \left(t\right)$ is not defined for values of $\left(1 - {2}^{t}\right) < 0$

That is
$g \left(t\right)$ is only defined if $\left(1 - {2}^{t}\right) \ge 0$
or
$t \le 1$

The Domain of $g \left(t\right)$ is $t \epsilon \left(- \infty , 1\right]$