Determine I) the Domain of the Function, Ii) the Range $$f ( x ) = \frac { 4 } { 6 x + 5 }$$

question 346

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.
- $$f ( x ) = \frac { 4 } { 6 x + 5 }$$

• A) \(f ( x ) : D = \left\{ x \mid x \neq \frac { 2 } { 3 } \right\} , R = \left\{ y \mid y \neq \frac { 4 } { 5 } \right\}\);
• \(f ^ { - 1 } ( x ) : D = \left\{ x \mid x \neq \frac { 4 } { 5 } \right\} , R = \left\{ y \mid y \neq \frac { 2 } { 3 } \right\}\)
• B) \(f ( x ) : D = \left\{ x \mid x \neq \frac { 5 } { 6 } \right\} R = \{ y \mid y \neq - 5 \}\);
• \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } | \mathrm { x } \neq - 5 \rangle , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 5 } { 6 } \right\} \right.\)
• C) \(f ( x )\) : \(D\) is all real numbers, \(R\) is all real number:
• \(\mathrm { f } ^ { - 1 } ( \mathrm { x } )\) : \(\mathrm { D }\) is all real numbers, \(R\) is all real numbe
• D) \(f ( x ) : D = \left\{ x \mid x \neq - \frac { 5 } { 6 } \right\} , R = \{ y \mid y \neq 0 \}\)
• \[\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } \neq 0 \} , \mathrm { R } = \left\{ \mathrm { y } \mid \mathrm { y } \neq - \frac { 5 } { 6 } \right\}\] ;

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