Question 1091038
let y = f(x).


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)


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