Why Isn't the Answer to the Hyperbolic Function e^10x?

[bobsmith76]

Homework Statement

why is the answer not e^10x ?

If you ignore the e's it should be

5x - 5x + 5x - - 5x, or
5x - 5x + 5x + 5x, which is 10x

 

[Dickfore]

If you ignored the e's, it wouldn't be a hyperbolic function, but a linear function.

 

[bobsmith76]

well, i still don't see any reason why the answer is not e^10x

 

[Dickfore]

Hint:

<br /> e^{x} + e^{y} \neq e^{x + y}<br />

For example: Take x = y = 0 and compare the two sides of this unequality.

 

[Curious3141]

Bob, this is basically \frac{a+b}{2} + \frac{a-b}{2} = \frac{a}{2} + \frac{b}{2} + \frac{a}{2} - \frac{b}{2} = (2)(\frac{a}{2}) = a. Simple algebra. Here a = e^{5x} and b = e^{-5x}.

But your comment indicates a deeper confusion about exponents and algebraic principles. I would suggest that it might be a good idea to review basic algebra including the rules of exponentiation.