Hyperbolic Function Question

**mr_motivator** · February 5th 2009, 04:09 PM

Not sure how to go about this question...

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

Thanks.

**Danny** · February 5th 2009, 04:16 PM

Originally Posted by mr_motivator

Not sure how to go about this question...

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

Thanks.

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

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

so

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

or

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

or

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

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

**TKHunny** · February 6th 2009, 06:40 PM

Originally Posted by mr_motivator

Not sure how to go about this question...

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.

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