equation becomes y = x^3 - 2
replace y with x and x with y and the equation becomes x = y^3 - 2
that is the inverse equation.
you can solve it for x or you can leave it as is, and graph it.
some software allows you to graph it as is.
other software requires you to solve it for y.
you can also graph it manually but that's labor intensive.
i graphed it both ways (as is) and after solving for y just to show you it's the same graph.
i also graphed the original equation and y = x.
if it is the inverse equation, then it will be a reflection o the original equation about the line y = x.
i also graphed the line y = -x + 8.
this line is perpendicular to the line y = x and shows two selected points, one on the original equation and one on the inverse equation, that show they are reflections about the line y = x because (x,y) on the original equation is equal to (y,x) on the inverse equation.
check out the graph to see what i mean.
the equations in blue are the inverse equations.
the original equation is red.
(x+2)^(1/3) is the same as the cube root of (x+2).
solving for y, start with x = y^3 - 2
add 2 to both sides of the equation to get x+2 = y^3
take the cube root of both sides of the equation to get y = cube root of (x+2).
here's the graph.
