Answer
$\{t\in R: t\geq -1\}=[-1 , \infty)$
Work Step by Step
The domain of $f(t)=\sqrt {t+1}$ is the set of all real numbers $t$ for which $\sqrt{t+1}$ is defined as a real number. We know the sqare root of a negative number is not defined, so the domain of $f(t)=\sqrt{t+1}$ is all real numbers $t$ for which $t+1 \geq 0$. We subtract $1$ from both sides to get $$t \geq -1.$$ Thus the domain of this function is all real numbers $t$ for which $t\geq -1$
In set notation, the domain is $\{t\in R: t\geq -1\}.$
In interval notation, the domain is $[-1 , \infty).$
