Determine Whether the Given Function Is One-To-One $$f ( x ) = \frac { 3 x + 8 } { - 6 x - 2 }$$

question 57

Multiple Choice

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
- $$f ( x ) = \frac { 3 x + 8 } { - 6 x - 2 }$$

• A) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 3 \mathrm { x } + 8 } { - 6 \mathrm { x } - 2 }\)
• B) \(f ^ { - 1 } ( x ) = \frac { 2 x + 8 } { - 6 x - 3 }\)
• C) Not a one-to-one function
• D) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - 6 \mathrm { x } - 3 } { 2 \mathrm { x } + 8 }\)

---

Definitions:

Secondary Circular Reactions

Repetitive actions in infants (4-8 months old) focused on external objects as a means to learn about their environment.

Coordination

The capacity to coordinate various body parts seamlessly and effectively.

Internalization of Schemes

The process by which individuals absorb and integrate new information into existing cognitive frameworks or structures, as proposed by Jean Piaget.

Object Permanence

The understanding that objects continue to exist even when they cannot be observed, seen as a key developmental milestone in infants.