Use a Graphing Calculator to Graph the Function Using the Given

question 288

Multiple Choice

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

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Definitions:

Detecting Changes

The process of identifying differences or modifications in conditions, situations, or variables over time.

Low-Frequency

Referring to something that occurs or is present at small or infrequent intervals; in physics, it relates to waves with relatively long wavelengths.

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The membrane within the cochlea of the inner ear that vibrates in response to sound, playing a critical role in hearing.

Vestibular System

The sensory system that contributes to balance, spatial orientation, and the coordination of movement.