Answer
Domain: $(-\infty,\ \frac{1}{2})$
Work Step by Step
We are asked to find the domain of:
$f(x)=10^{x^{2}}+\log(1-2x)$
We can't take a log of a negative number (or 0), so:
$1-2x\gt 0$
$-2x\gt -1$
$x\lt \frac{1}{2}$
Therefore, the domain is: $(-\infty,\ \frac{1}{2})$
