You can put this solution on YOUR website! y=sqrt(5+8x), and the domain is x=-5/8
x=sqrt(5+8y)
x^2=5+8y
8y=x^2-5
y=(1/8)(x^2-5) with the range restricted to the domain x>=-5/8
This function is one for which there is an easy alternative to the standard method for finding an inverse.
The given function does the following to the input:
(1) multiply by 8
(2) add 5
(3) take the square root
The inverse function has to "get you back where you started"; to do that, it has to perform the opposite operations on the input, in the reverse order:
(1) square it
(2) subtract 5
(3) divide by 8
The inverse function is
Of course the domain of the function is restricted by the restriction on the domain of the given function.