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

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) $f ( x ) : D = \left\{ x \mid x \neq \frac { 1 } { 4 } \right\} , R = \left\{ y \mid y \neq \frac { 1 } { 3 } \right\}$
$$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 3 } \right\} , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 1 } { 4 } \right\}$$