Answer
one-to-one function
inverse: $f^{-1}(x)=\sqrt[3]{x+4}$
Work Step by Step
Some of the ordered pairs of the given function, $
f(x)=x^3-4
$, are $
\left\{(-2,-12)(-1,-5),(0,-4),(1,-3),(2,4),...\right\}
$. Note that every $y$-coordinate from this function is unique. Hence, the given function is a one-to-one function.
To find the inverse, let $y=f(x)$. Then, interchange the $x$ and $y$ variables and solve for $y$. That is,
\begin{align*}\require{cancel}
y&=x^3-4
\\&\Rightarrow
x=y^3-4
&(\text{interchange $x$ and $y$})
\\&
x+4=y^3
&(\text{solve for $y$})
\\&
\sqrt[3]{x+4}=y
\\&
y=\sqrt[3]{x+4}
.\end{align*}
Hence, the inverse is $
f^{-1}(x)=\sqrt[3]{x+4}
$.
