1. ## Hyperbolic Function Question

How many solutions does the equation -6 sinh(x) = 9 have?

Thanks.

2. Originally Posted by mr_motivator

How many solutions does the equation -6 sinh(x) = 9 have?

Thanks.
Easiet way is to graph $\displaystyle y = \sinh x\;\;\; \text{and}\;\;\; y = -\frac {3}{2}$ and look for intersection points. To find them, replace

$\displaystyle \sinh x = \frac{e^x - e^{-x}}{2}$

so

$\displaystyle \frac{e^x - e^{-x}}{2} = -\frac{3}{2}$

or

$\displaystyle e^x + 3 - e^{-x} = 0$

or

$\displaystyle \left(e^x\right)^2 + 3 e^x - 1 = 0$

Now this is a quadratic in $\displaystyle e^x$. Yours from here.

3. Originally Posted by mr_motivator

How many solutions does the equation -6 sinh(x) = 9 have?

Thanks.
Trivial Question. This is a thought problem.

f(x) = -6sinh(x) is an odd function - frankly, monotonic decreasing.

f(x) = 9 is constant

There is 1 solution.

Done. Reach out and grab easy ones. You still have to explain it for your final grade. Good luck with that.