Originally Posted by

**BlackBlaze** I'm getting spoonfed instructions and I still don't get it. >_>

I am to find the inverse of f(x) = x^3 + x, by using properties of sinh(x).

The question tells me to let y = x^3 + x, let z = $\displaystyle \frac{3\sqrt{3}}{2}x$ and then prove that $\displaystyle \frac{3\sqrt{3}}{2}y = 4z^3 + 3z$.

After I do that, it tells me to set z = sinh(θ), solve for θ and then reverse the changes to the variables to find x as a function of y.

I managed to do most of it, up until the 'reverse the changes' part. My θ equals something ridiculously long and confusing, and I have no idea how to use it to my benefit.

$\displaystyle \theta = \frac{sinh^{-1}(\frac{3\sqrt{3}}{2}y)}{3}$

Just need a bit of guiding light, it feels like I overlooked something...

EDIT: All right, well, I solved for θ in terms of x now too.

$\displaystyle \theta = sinh^{-1}(\frac{\sqrt{3}}{2}x)$

And then I equate the two.

$\displaystyle sinh^{-1}(\frac{\sqrt{3}}{2}x) = \frac{sinh^{-1}(\frac{3\sqrt{3}}{2}y)}{3}$

And I'm not exactly sure how to solve...