Show Algebraically That the Functions $f$ And $g$ Shown Below Are Inverse Functions

question 78

Multiple Choice

Show algebraically that the functions $f$ and $g$ shown below are inverse functions.
$f ( x ) = \sqrt [ 3 ] { 8 x - 7 } , \quad g ( x ) = \frac { x ^ { 3 } + 7 } { 8 }$

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Definitions:

Reciprocal Determinism

A concept in psychology that suggests a person's behavior is influenced by both their personal characteristics and their environment in a mutual way.

Maturity Principle

The concept that individuals become more conscientious and agreeable as they age, showing fewer negative or antisocial behaviors.

Self-Serving Bias

The common human tendency to attribute personal successes to internal factors while blaming failures on external factors.

Narcissism

A psychological condition characterized by self-centeredness, a lack of empathy for others, and an excessive need for admiration.