Answer
a) $f(-12)\approx -1.919$
b) $x\approx -77364.094$
Work Step by Step
Given $$f(x)=\sqrt[5]{x-14}= \left( x-14 \right)^{\frac{1}{5}}.\tag{1}$$a) Set $x= -12$ in equation $(1)$ and determine $f(-12)$:
\begin{equation}
\begin{aligned}
f(-12)&= \left(-12-14 \right)^{\frac{1}{5}} \\
&= \left( -26 \right)^{\frac{1}{5}} \\
&\approx -1.919.
\end{aligned}
\end{equation} b) Set $f(x)=-9.5$ in equation $(1)$ and solve for $x$:
\begin{equation}
\begin{aligned}
f(x) & =-9.5 \\
\left( x-14 \right)^{\frac{1}{5}} & =-9.5 \\
\left(\left( x-14 \right)^{\frac{1}{5}} \right)^5& = \left(-9.5\right)^5\\
x-14 &=-77378.09375\\
x&= -77378.09375+14\\
x&\approx -77364.094.
\end{aligned}
\end{equation}
