Question 588089
Problem: Find the inverse of {{{y = x^2 + sqrt(x)}}}
:
You seem to have exhausted the usual methods, so I tried this approach
I don't think there is an inverse, anyway
The table for the original equation
 x | y
-------
 1 | 2
 4 |18
 9 |84
:
Swapping x & y
 x | y
-------
 2 | 1
18 | 4
84 | 9
After some tedious math, solving for a, b, c in the y = ax^2+bx+c, I came up with an even more tedious equation
y = -.005452x^2 + .4952x + .5759
A graph kind of shows an inverse, but negative value probably make it invalid
plus the quadratic equation will curve back towards 0
{{{ graph( 300, 300, -20, 20, -20, 20, x^2+sqrt(x), -.001363x^2+.21476x+.5759) }}}
:
After I finished this I thought it was kind of silly, and was not going to bother sending it, but you can just toss in the usual place of rejected stuff. 
C