# Chapter 10 - Exponents and Radicals - 10.1 Radical Expressions and Functions - 10.1 Exercise Set: 103

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 $\text{ all real numbers .}$

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