Question 919876
The roles of domain and range are switched from function to inverse.
Your given functional-form equation to start with is the upper half of a parabola with a horizontal symmetry axis.
Try completing-the-square to have a better understanding of your given parabola.


{{{x^2-5x-6+(5/2)^2-(5/2)^2}}}
{{{x^2-5x+(5/2)^2-6-(5/2)^2}}}
{{{(x-5/2)^2-6-25/4}}}
{{{(x-5/2)^2-24/4-25/4}}}
{{{(x-5/2)^2-49/4}}}


Now, what you are starting with is {{{highlight_green(y=sqrt((x-5/2)^2-49/4))}}}.
The vertex for this given equation is (5/2,-49/4).
The shape is horizontal parabola.
DOMAIN:  x values must be greater than 5/2.
RANGE:  y values are greater than or equal to -49/4.


If you want to now use the simple method of just switching x and y roles in the given equation, you can; and just solve that for y; and remember you must choose the RIGHT-HAND branch of the function.