#### Answer

all real numbers

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
The domain of the given function, $
f(t)=7+\sqrt[8]{t^8}
,$ is the permissible values of $x.$
$\bf{\text{Solution Details:}}$
Since $\sqrt[n]{x^n}=|x|$ if $n$ is even and $\sqrt[n]{x^n}=x$ if $n$ is odd, then $
\sqrt[8]{t^8}
,$ is defined for any value of $t.$ Hence, the domain is the set of $\text{
all real numbers
.}$