Find the Inverse of the Given Function and Express It $y = f ^ { - 1 } ( x )$

question 50

Multiple Choice

Find the inverse of the given function and express it in the form $y = f ^ { - 1 } ( x )$ . Verify the result by showing that $\left( f \circ f ^ { - 1 } \right) ( x ) = \left( f ^ { - 1 } \circ f \right) ( x ) = I ( x )$ . $f ( x ) = \frac { 2 x + 10 } { 5 }$

• A) \(f ^ { - 1 } ( x ) = 5 x - 2\)
• B) \(f ^ { - 1 } ( x ) = \frac { 5 } { 2 } x - 5\)
• C) \(f ^ { - 1 } ( x ) = \frac { 2 } { 5 } x + 2\)
• D) \(f ^ { - 1 } ( x ) = \frac { 5 } { 2 } x + 5\)
• E) \(f ^ { - 1 } ( x ) = 2 x + 5\)

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Definitions:

Cooley

Charles Horton Cooley was an American sociologist who is best known for his concept of the looking-glass self, which describes the process by which individuals base their sense of self on how they believe others view them.

Looking-Glass Self

A concept in sociology suggesting that an individual's self-image is shaped by how others perceive them, acting as a reflective social mirror.

Abstract Moral Stage

A theoretical phase in moral development characterized by an understanding of ethical principles that transcend personal interests or societal conventions.

Ego Control

A psychological concept referring to an individual's ability to regulate their impulses, emotions, and behaviors in accordance with societal norms.