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.
-$$f ( x ) = x ^ { 4 } - 6 x ^ { 2 } + 5 ; [ - 3,3 ] \text { by } [ - 40,40 ]$$
A) one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 4 ] { \mathrm { x-5 } }$
B) one-to-one; $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { 6 x ^ { 2 } - 5 }$
C) one-to-one: $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { x - 5 } + 6 x ^ { 2 }$
D) not one-to-one

Question

Quizplus · Accepted Answer

The function $f(x) = x^4 - 6x^2 + 5$ is not one-to-one because it does not pass the horizontal line test. For any given y-value, there can be more than one x-value. This is due to the symmetry and shape of the graph of a quartic function with even powers of x.

Use a Graphing Calculator to Graph the Function Using the Given