Find the Inverse Function of F $$f ( x ) = \frac { 3 x - 2 } { x + 5 }$$

question 334

Multiple Choice

Find the inverse function of f. State the domain and range of f.
- $$f ( x ) = \frac { 3 x - 2 } { x + 5 }$$

• A) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 5 } { 3 \mathrm { x } - 2 }\); domain of \(\mathrm { f } : \{ \mathrm { x } \mid \mathrm { x } z - 5 \}\); range of \(\mathrm { f } : \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 2 } { 3 } \right\}\)
• B) \(f ^ { - 1 } ( x ) = \frac { 5 x + 2 } { 3 + x }\); domain of \(f : \{ x \mid x \neq - 5 \}\); range of \(f : \{ y \mid y \neq - 3 \}\)
• C) \(f ^ { - 1 } ( x ) = \frac { 3 x + 2 } { x - 5 }\); domain of \(f : \{ x \mid x \neq - 5 \}\); range of \(f : \{ y \mid y \neq 5 \}\)
• D) \(f ^ { - 1 } ( x ) = \frac { 5 x + 2 } { 3 - x }\); domain of \(f : \{ x \mid x \neq - 5 \}\); range of \(f : \{ y \mid y \neq 3 \}\)

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Definitions:

Ownner's Equity

The portion of a company's assets that belongs to the owners or shareholders after liabilities are subtracted; also known as shareholder's equity.

Total Liabilities

The combined amount of obligations a company owes to external parties, including loans, accounts payable, mortgages, and other debts due within one year or beyond.

Owner's Equity

The residual interest in the assets of the entity after subtracting liabilities, representing the owner's claim on the business assets.

Total Assets

The sum of all assets owned by a company, including cash, investments, property, and equipment.