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 $\mathrm { f } : \{ \mathrm { x } \mid \mathrm { x } \neq - 5 \}$; range of $\mathrm { f } : \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 2 } { 3 } \right\}$

B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 5 \mathrm { x } + 2 } { 3 + \mathrm { x } }$; domain of $\mathrm { f } : \{ \mathrm { x } \mid \mathrm { x } \neq5 \}$; range of $\mathrm { f } : \{ \mathrm { y } \mid \mathrm { y } \neq 3 \}$

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 $f : \{ y \mid y \neq 3 \}$

Question

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 $\mathrm { f } : \{ \mathrm { x } \mid \mathrm { x } \neq - 5 \}$; range of $\mathrm { f } : \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 2 } { 3 } \right\}$

B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 5 \mathrm { x } + 2 } { 3 + \mathrm { x } }$; domain of $\mathrm { f } : \{ \mathrm { x } \mid \mathrm { x } \neq5 \}$; range of $\mathrm { f } : \{ \mathrm { y } \mid \mathrm { y } \neq 3 \}$

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 $f : \{ y \mid y \neq 3 \}$

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. For $f(x) = \frac{3x - 2}{x + 5}$, setting $y = \frac{3x - 2}{x + 5}$ and solving for $x$ in terms of $y$ gives $x = \frac{5y + 2}{3 - y}$, which is the inverse function. The domain of $f$ excludes $x = -5$ to avoid division by zero, making the range of $f$ all real numbers except $y = \frac{2}{3}$, which is the horizontal asymptote of $f$, not directly related to the choices given.

Find the Inverse Function of F f(x)=3x−2x+5f ( x ) = \frac { 3 x - 2 } { x + 5 }f(x)=x+53x−2​

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