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