Show that if a 0 and b 0, then there exist numbers a and such that aex be x equals either or sinh(x ) or cosh(x ), In other words, almost every function of the form f(x) aex be x is a shifted and stretched hyperbolic sine or cosine function

Question: Show that if a 0 and b 0, then there exist numbers a and such that aex + be-x equals either or

Show that if a ≠ 0 and b ≠ 0, then there exist numbers a and β such that aex + be-x equals either or α sinh(x + β) or α cosh(x + β), In other words, almost every function of the form f(x) = aex + be-x is a shifted and stretched hyperbolic sine or cosine function.

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