#### Answer

Domain: $(-\infty,\ \infty)$

#### Work Step by Step

We are given:
$f(t)=\sqrt[3]{t-1}$
The domain of a function consists of all values that $x$ is allowed to have. In this case, there are no restrictions on $x$ (we can take the cube root of positive and negative values).
Thus the domain is: $(-\infty,\ \infty)$