Reparametrize the x = e^t, y = sqrt(2) t, z = -e^(-t) in terms of arc length measured from the point where t = 0.

Here is my attempt: http://f.imgtmp.com/Iam48.jpg

Any help would be greatly appreciated!
Thanks in advance!

Question

Reparametrize the x = e^t, y = sqrt(2) t, z = -e^(-t) in terms of arc length measured from the point where t = 0.

Here is my attempt: http://f.imgtmp.com/Iam48.jpg

Any help would be greatly appreciated!
Thanks in advance!

s3a · Answer

I'm trying to get t(s) from s(t).

s3a · Answer

Wolfram alpha confirms the solution exists in the domain of reals.

s3a · Answer

Firstly, am I even attempting the problem correctly?