Answer
a) $[2, \infty)$
b) $(-\infty, \infty)$
Work Step by Step
a) For this function, the domain is any $t$ value that creates a zero or positive value in the square root.
$10^t-100\ge0$
$10^t\ge100$
$t\ge2$
b) $\sin{x}$ exists for all real numbers, so it doesn't matter what we plug in for $t$. As a result, the domain is all real numbers.
