Answer
a) $f(-60)\approx -1.694$
b) $x= -2207$
Work Step by Step
Given $$f(x)=\sqrt[7]{x+20}= \left( x+20 \right)^{\frac{1}{7}}.\tag{1}$$ a) Set $x= -60$ in equation $(1)$ and determine $f(-60)$:
\begin{equation}
\begin{aligned}
f(-60)&= \left( -60+20 \right)^{\frac{1}{7}} \\
&= \left( -40 \right)^{\frac{1}{7}} \\
&\approx -1.694.
\end{aligned}
\end{equation} b) Set $f(x)=-3$ in equation $(1)$ and solve for $x$: \begin{equation}
\begin{aligned}
f(x) & =-3 \\
\left( x+20 \right)^{\frac{1}{7}} & =-3 \\
\left(\left( x+20 \right)^{\frac{1}{7}} \right)^7& = \left(-3\right)^7\\
x+20 &=-2187\\
x&= -2187-20\\
x&= -2207.
\end{aligned}
\end{equation}
