Determine I) the Domain of the Function, Ii) the Range $$f ( x ) = \frac { 3 } { x - 1 }$$

question 435

Multiple Choice

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of
the inverse.
- $$f ( x ) = \frac { 3 } { x - 1 }$$

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

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Definitions:

Subsequent Holder

An individual or entity that obtains a negotiable instrument after its initial issuance, under certain conditions that preserve the instrument's negotiable status.

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A primary obligation of a third party to pay a debt along with the debtor

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The right of the insurer upon payment to take over the rights of the insured in relation to whoever caused the injury.

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A person assuming obligation to pay if the debtor does not.