How do you find the Domain of the function f(x) = 1/(2-e^x)?

Apr 7, 2015

$f \left(x\right) = \frac{1}{2 - {e}^{x}}$
is defined for all Real values of $x$ except when $2 = {e}^{x}$

If ${e}^{x} = 2$
then
$\ln \left({e}^{x}\right) = \ln \left(2\right)$
$x = \ln \left(2\right)$

So the given function $f \left(x\right)$ has a Domain of all Real numbers except
$\ln \left(2\right)$