- #1
j3dwards
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Homework Statement
Split the function f(x) = ex + 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:
ex = 0.5[ex - e-x] + 0.5[ex + 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?