# Hyperbolic functions

1. Feb 8, 2012

### bobsmith76

1. The problem statement, all variables and given/known data

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

2. Feb 8, 2012

### Dickfore

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

3. Feb 8, 2012

### bobsmith76

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

4. Feb 8, 2012

### Dickfore

Hint:

$$e^{x} + e^{y} \neq e^{x + y}$$

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

5. Feb 8, 2012

### 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.