Chapter 6 - Linear Transformations - 6.1 Introduction to Linear Transformations - 6.1 Exercises - Page 301: 63

$-\cos x+C$

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