The Function F Is One-To-One $$f ( x ) = \frac { 1 } { 4 x + 3 }$$

question 122

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.
- $$f ( x ) = \frac { 1 } { 4 x + 3 }$$

• A) \(f ( x ) : D = \left\{ x \mid x \neq \frac { 3 } { 4 } \right\} , R = \{ y \mid y \neq - 3 \}\);
• \[\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } | \mathrm { x } \neq - 3 \rangle , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 3 } { 4 } \right\} \right.\]
• B) \(f ( x ) : D = \left\{ x \mid x z - \frac { 3 } { 4 } \right\} , R = \{ y \mid y \neq 0 \}\);
• \[f ^ { - 1 } ( x ) : D = \{ x \mid x \neq 0 \} , R = \left\{ y \mid y \neq - \frac { 3 } { 4 } \right\}\]
• 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) \(f ( x ) : D = \left\{ x \mid x \neq \frac { 1 } { 4 } \right\} , R = \left\{ y \mid y \neq \frac { 1 } { 3 } \right\}\)
• \[\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 3 } \right\} , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 1 } { 4 } \right\}\]

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