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) \(f ( x ) : D = \{ x \mid x \neq 3 \} , R = \{ y \mid y \neq - 1 \}\);
• \[\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } z - 1 \} , \mathrm { R } = \{ \mathrm { y } \mid \mathrm { y } \neq 3 \}\]

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Definitions:

Assumption of the Risk

Assumption of the risk is a legal doctrine whereby an individual acknowledges and accepts the known risks associated with an activity, often relieving another party of liability for harm that may result.

Liability

The state of being responsible for something, especially by law, including debts or legal obligations.

Harm

Damage or injury that affects someone or something in a negative way, including physical, psychological, financial, or reputational impacts.

Inherently Dangerous

Activities or conditions that carry a significant risk of harm to people or property by their nature.