Question

Determine the inverse of f(x) = x^3 - x^2 - 2x show steps

Answer 1

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