Chapter 6 - Linear Transformations - 6.1 Introduction to Linear Transformations - 6.1 Exercises - Page 301: 64

$\ln{|x|}+C$

We know from the exercise that $D_x(f(x))=\frac{1}{x}$. The pre-image here is the "inverse" of the derivative; thus we can obtain it by integrating $\frac{1}{x}$ with respect to $x$, which is $\ln{|x|}+C$, where $C$ is a constant.