- #1

j3dwards

- 32

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## Homework Statement

Split the function f(x) = e

^{x}+ πe

^{−x}into odd and even parts, and express your result in terms of cosh x and sinh x.

## Homework Equations

f(x) = 0.5[f(x) + f(-x)] +0.5[f(x) - f(-x)]

## The Attempt at a Solution

So i know that:

e

^{x}= 0.5[e

^{x}- e

^{-x}] + 0.5[e

^{x}+ e

^{-x}] = sinh(x) + cosh(x)

So let the even part be a(x) and the odd be b(x).

a(x) = cosh(x) + πcosh(x) = (1 + π) cosh(x)

b(x) = sinh(x) - πsinh(x) = (1 - π) sinh(x)

Is this correct?