Find the Inverse of the Function $$f ( x ) = 5 ^ { x }$$

question 175

Multiple Choice

Find the inverse of the function.
- $$f ( x ) = 5 ^ { x }$$

• A) \(f ^ { - 1 } ( x ) = \log _ { 5 } x\)
• B) \(f ^ { - 1 } ( x ) = x ^ { 5 }\)
• C) \(f ^ { - 1 } ( x ) = \ln ( 5 x )\)
• D) \(f ^ { - 1 } ( x ) = \log _ { x } 5\)

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Definitions:

Dominant Strategies

In game theory, strategies that result in the best possible outcome for a player, regardless of the actions taken by other players.

Backward Induction

A method used in game theory and decision-making processes that involves reasoning backwards from the end of a problem or scenario to determine a sequence of optimal actions.

Extensive Form

A representation of a game that displays the sequences of choices available to players, including their possible strategies and outcomes.

Nash Equilibrium

A concept in game theory where no player can gain by changing their strategy while the other players keep theirs unchanged, indicating optimal decision-making among competitors.