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.
-$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - x + 3 ; [ - 2,4 ]$ by $[ - 20,20 ]$
A) one-to-one; $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 3 } - x$
B) not one-to-one
C) one-to-one; $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 3 }$
D) one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } ^ { 2 } - 3 \mathrm { x } + 3 }$

Question

Quizplus · Accepted Answer

The function $f(x) = x^3 - 3x^2 - x + 3$ is a cubic polynomial, which typically has regions where it increases and decreases. This means it can fail the Horizontal Line Test, indicating it is not one-to-one within the given viewing window.

Use a Graphing Calculator to Graph the Function Using the Given