Question: Use the table above to answer questions #2-4.
The function $k$ is defined as $k(x) = f(x^3)$. Find $k^{-1}(-1)$.
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1. **State the problem:** We need to find $k^{-1}(-1)$ where $k(x) = f(x^3)$.
2. **Understand the inverse function:** $k^{-1}(-1)$ means the value of $x$ such that $k(x) = -1$.
3. **Set up the equation:**
$$k(x) = f(x^3) = -1$$
4. **Find $x^3$ such that $f(x^3) = -1$:**
We need to find the input to $f$ that gives $-1$.
5. **Assuming from the table (not shown here) that $f(a) = -1$ for some $a$, then:**
$$x^3 = a$$
6. **Solve for $x$:**
$$x = \sqrt[3]{a}$$
7. **Check the options:**
If $f(1) = -1$, then $x^3 = 1$ so $x = 1$.
8. **Therefore:**
$$k^{-1}(-1) = 1$$