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Jen was asked to determine whether $f(x)=\frac{1}{\sqrt[3]{x}}$ is even, odd, or neither. Here is her work:$\newline$Step $1$: Find expression for $f(-x)$$\newline$$$\begin{aligned} f(-x) & =\frac{1}{\sqrt[3]{(-x)}} \\ & =\frac{1}{\sqrt[3]{-1} \cdot \sqrt[3]{x}} \\ & =-\frac{1}{\sqrt[3]{x}} \end{aligned}$$$\newline$Step $2$: Check if $f(-x)$ is equal to $f(x)$ or $-f(x)$$\newline$$-\frac{1}{\sqrt[3]{x}}$ is the same as$\newline$$$-f(x)=-\frac{1}{\sqrt[3]{x}} .$$$\newline$Step $3$: Conclusion$\newline$$f(-x)$ is equivalent to $-f(x)$, so $f$ is even.$\newline$Is Jen's work correct? If not, what is the first step where Jen made a mistake?$\newline$Choose $1$ answer:$\newline$(A) Jen's work is correct.$\newline$(B) Jen's work is incorrect. She first made a mistake in Step $1$.$\newline$(C) Jen's work is incorrect. She first made a mistake in Step $2$.$\newline$(D) Jen's work is incorrect. She first made a mistake in Step $3$.