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; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 4 ] { 6 \mathrm { x } ^ { 2 } - 5 }$
B) one-to-one; $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { x - 5 } + 6 x ^ { 2 }$
C) one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 4 ] { \mathrm { x } - 5 }$
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 within the given viewing window. A graph of this function would show that for some values of $y$, there are multiple $x$ values, indicating it is not one-to-one.

Use a Graphing Calculator to Graph the Function Using the Given