Find all exact values of http://stuff.daniel15.com/cgi-bin/mathtex.cgi?a for which http://stuff.daniel15.com/cgi-bin/ma...sqrt%7B2x-3%7D is always an increasing function.

My working:

First notice the domain: http://stuff.daniel15.com/cgi-bin/ma...%20%5Cinfty%29

We require all http://stuff.daniel15.com/cgi-bin/ma...x%29%20%3E%200 for all x within this domain.

Thus http://stuff.daniel15.com/cgi-bin/ma...t%7B2x-3%7D%7D

Here we place a restriction on the original domain for http://stuff.daniel15.com/cgi-bin/ma...%20%5Cinfty%29 [since http://stuff.daniel15.com/cgi-bin/ma...%7B3%7D%7B2%7D, because derivative is not defined at this point]

Thus http://stuff.daniel15.com/cgi-bin/ma...3%7D%20%3E%200 for all http://stuff.daniel15.com/cgi-bin/ma...%20%5Cinfty%29

Thus we now need to ensure http://stuff.daniel15.com/cgi-bin/ma...%201%20%3E%200

Solving for x = 0 yields:

http://stuff.daniel15.com/cgi-bin/ma...%7D%7D%7B10%7D

Notice http://stuff.daniel15.com/cgi-bin/ma...elta%20%3E%200 ie http://stuff.daniel15.com/cgi-bin/ma...a+56%20%3E%200 for all a

Now what?