Write an Equation of the Inverse for the One-To-One Function $$f ( x ) = 5 x ^ { 3 } - 5$$

question 21

Multiple Choice

Write an equation of the inverse for the one-to-one function $$f ( x ) = 5 x ^ { 3 } - 5$$

• A) \(f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x + 5 } { 5 } }\)
• B) \(f ^ { - 1 } ( x ) = \left( \frac { x + 5 } { 5 } \right) ^ { 3 }\)
• C) \(f ^ { - 1 } ( x ) = \frac { x - 5 } { 5 }\)
• D) \(f ^ { - 1 } ( x ) = \frac { x + 5 } { 5 }\)

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Definitions:

Mental Representation

The internal depiction of information in the mind, such as images, words, or concepts.

Object Permanence

The understanding that objects continue to exist even when they cannot be seen, heard, or otherwise sensed, a concept that develops in infancy.

Conservation

In cognitive development, the understanding that certain properties of objects remain the same, despite changes in the object's appearance.

Egocentrism

A cognitive characteristic in which an individual is unable to differentiate between their own perspective and that of another person.