Chapter 13, Problem 18PS

To determine

To prove: The function $u\left(x,t\right)=\frac{1}{2}\left[f\left(x-ct\right)+f\left(x+ct\right)\right]$ is a solution to the one-dimensional wave equation, $\frac{{\partial }^{2}u}{\partial t^2}=c^2\frac{{\partial }^{2}u}{\partial x^2}$.