Chapter 1.6, Problem 53E

To determine

Prove thatevery function $f$ can be written as a sum in the form $f\left(x\right)=f_{+}\left(x\right)+f_{-}\left(x\right)$ where $f_{+}\left(x\right)$ is an even function and $f_{-}\left(x\right)$ is an odd function and also express $f\left(x\right)=5e^x+8e^{-x}$ in terms of $\cosh x$ and $\sinh x$.