Chapter 6 - Vector Spaces - 6.2 Linear Independence, Basis, and Demension - Exercises for 6.2 - Page 457: 12

This set of functions is linearly independent.

To show that a set of two functions is linearly independent, show that one vector isn't a scalar multiple of the other. Since $e^x$ is not a scalar multiple of $e^{-x}$, $\{e^x, e^{-x}\}$ are linearly independent.