Switch the x and y values to find the inverse.
y=x−3x+2
The inverse is given by
x=y−3y+2
Solve for y now:
x(y+2)=y−3
xy+2x=y−3
2x+3=y−xy
2x+3=y(1−x)
2x+31−x=y
The inverse, f−1(x), is given by f−1(x)=2x+31−x.
The function can be graphed using knowledge of asymptotes, invariant points, and intercepts. Prepare a table of values for f(x). Recall that f−1(x) is simply a transformation of(x) over the line y=x, so f−1(x) has a table of values where X and y are inverted relative to f(x).
For example, if the point (2,3) belongs on the graph of f(x), the point (3,2) belongs on f−1(x).
Replace
F(X)FX with
yy.
y=X3+2X−3Xy=X3+2X-3XInterchange the variables.
X=y3+2y−3yX=y3+2y-3y
