Question

Invert \(2e^x-\frac{1}{e^x}\).

Answer 1

Inverse of \(2y-\frac{1}{y}\).

Answer 2

okay suppose
X=2y-1/y

Answer 3

oh u make e^x=y

Answer 4

and no need for that stuff

Answer 5

just say y=2*e^x - 1/e^x

solve for x in terms of y

Answer 6

I know that but what are the steps? Wolfram Alpha gives \(\log\left(\frac{1}{4}(x-\sqrt{x^2+8}\right)\) but I have no idea where that came from.

Answer 7

okay

Answer 8

lets work it out

Answer 9

actually im more comfortable with the substitution u = e^x

Answer 10

hmm