start with y = x^2 + 4/3.
replace y with x and x with y to get x = y^2 + 4/3
subtract 4/3 from both sides of the equation to get x - 4/3 = y^2
take the square root of both sides of the equation to get y = plus or minus square root of (x - 4/3)
that should be your answer.
y = plus or minus sqrt(x - 4/3)
to show that these are inverse equations, then graph the original equation and graph the two inverse equations and then graph the line y = x and then graph the line y = -x + 5
if the equations are inverse, then they should be reflections about the line y = x.
if they are reflections about the line y = x, then their coordinates are interposed.
(x,y) on one side of the line y = x is the same distance from (y,x) on the other side of the line y = x.
this can be shown on the graph by using their intersections with the line y = -x + 5, with the 5 being arbitrarily chosen for clarity.
the graph is shown below:
you can see that the red line and blue line are reflections about the line y = x and you can see that the red line and the orange line are reflections about the line y = x.
the red line is y = x^2 + 4/3
the blue line is y = sqrt(x - 4/3)
the orange line is y = -sqrt(x - 4/3)
