Prove that any linear combination of e^x, e^-x can be written as f(x)=d*cosh(x-x0)

[BirgerBrosa]

This might be an easy question for some, but I just can't wrap my head around this. The problem is I don't really know how to start answering the question.

The question is as following:

Prove, through algebra, that any linear combination of the functions ex and e−x (for example: f(x)=a*e^x + b*e^-x) can be written as f(x)=d*cosh(x-x₀).

Hope someone can help me, I need it.

 

[Deleted member 4993]

This might be an easy question for some, but I just can't wrap my head around this. The problem is I don't really know how to start answering the question.

The question is as following:

Prove, through algebra, that any linear combination of the functions ex and e−x (for example: f(x)=a*e^x + b*e^-x) can be written as f(x)=d*cosh(x-x₀).

Hope someone can help me, I need it.

Please tell us the mathematical definition of cosh(x).