9/05/2014 Given y = 2/(ex + e-x), solve for x in terms of y.



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9/05/2014 Solution. Since y = 2/(ex + e-x), cross-multiplying, we get:

yex + ye-x = 2

Rewriting: yex + y· 1/ex = 2
Multiplying by the LCD of e
x to clear the fraction: ye2x + y = 2ex
Rewriting and rearranging: y(e
x)22ex + y = 0, which is a quadratic in ex.
Using the quadratic formula: e
x = [2 ± (4 – 4y2)] / 2y
Factoring out the 4 from inside the
and simplifying:
e
x = [1 ± (1 – y2)]/ y
so that switching to
log form: x = ln [(1 ± (1 – y2))/ y]