Determine Whether the Function Has an Inverse Function $g ^ { - 1 } ( x ) = \frac { 7 } { x }$

question 9

Multiple Choice

Determine whether the function has an inverse function.If it does,find the inverse function. ?
G(x) = x⁷
?

• A) \(g ^ { - 1 } ( x ) = \frac { 7 } { x }\)
• B)g^-1(x)= -7x
• C)? \[g ^ { - 1 } ( x ) = - \frac { x } { 7 }\]
• D)g^-1(x)= 7x
• E)The inverse exists,but none of the above

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Definitions:

Autonomy

The capacity to make an informed, uncoerced decision; often associated with self-governance and independence.

Individualistic Societies

Societies that emphasize personal achievements, individual rights, and autonomy, as opposed to collective goals.

Collectivistic Societies

Societies that prioritize the needs and goals of the group over the desires of the individual, emphasizing community, cooperation, and interdependence.

Relationship Orientations

The inclination or preference towards certain types of interactions or bonds with others, influencing personal connections.