The Function F Is One-To-One $$f ( x ) = \frac { 3 } { x + 1 }$$

question 31

Multiple Choice

The function f is one-to-one. State the domain and the range of f and f^-1. Write the domain and range in set-builder
notation.
- $$f ( x ) = \frac { 3 } { x + 1 }$$

• A) \(f ( x ) : D = \{ x \mid x \neq - 1 \} , R = \{ y \neq 0 \}\);
• \[f ^ { - 1 } ( x ) : D = \{ x \mid x \neq 0 \} , R = \{ y \mid y \neq - 1 \}\]
• B) \(f ( x )\) : D is all real numbers, \(R = \{ y | y \neq 3 \rangle\);
• \(f ^ { - 1 } ( x ) : D = \{ x \mid x \neq 3 \} , R\) is all real numbers
• C) \(f ( x )\) : \(D\) is all real numbers, \(R\) is all real numbers;
• \(\mathrm { f } ^ { - 1 } ( \mathrm { x } )\) : \(\mathrm { D }\) is all real numbers, \(\mathrm { R }\) is all real numbers
• D) \(f ( x ) : D = \{ x \mid x \neq 3 \} , R = \{ y \mid y \neq - 1 \}\);
• \[\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } z - 1 \} , \mathrm { R } = \{ \mathrm { y } \mid \mathrm { y } \neq 3 \}\]

---

Definitions:

Latin America

A region that includes countries in the Americas where Romance languages (primarily Spanish and Portuguese) are predominant.

Naive Psychologists

A term used to describe how ordinary people make sense of their own and others' behavior or actions as if they are amateur psychologists.

Interpersonal Relationships

Connections and interactions between two or more people, often based on emotional or social bonds.

Common Sense

Practical judgement concerning everyday matters, or a basic ability to perceive, understand, and judge things shared by nearly all people.