Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function
is one-to-one. If the function is one-to-one, give the equation of the inverse function.
-$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - x + 3 ; [ - 2,4 ] \text { by } [ - 20,20 ]$$
A) not one-to-one
B) one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } - 3 } - \mathrm { x }$
C) one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } ^ { 2 } - 3 \mathrm { x } + 3 }$
D) one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } - 3 }$

Question

Quizplus · Accepted Answer

The function $f(x) = x^3 - 3x^2 - x + 3$ is not one-to-one because a cubic function, especially one with a term that decreases the degree of $x$ (like $-3x^2$), typically has regions where it increases and decreases, violating the horizontal line test for one-to-one functions within the given viewing window.

Use a Graphing Calculator to Graph the Function Using the Given