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

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 $\mathrm { f } : \{ \mathrm { x } \mid \mathrm { x } z - 5 \}$; 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 $f : \{ y \mid y \neq 3 \}$

Quizplus · Accepted Answer

To find the inverse function $f^{-1}(x)$, we swap $x$ and $y$ in the original function and solve for $y$. Starting with $y = \frac{3x - 2}{x + 5}$, we swap to get $x = \frac{3y - 2}{y + 5}$ and solve for $y$, leading to $y = \frac{5x + 2}{3 - x}$. The domain of $f$ excludes $x = -5$ to avoid division by zero, and its range excludes $y = 3$ because there's no $x$ value that would make $f(x) = 3$, as seen from the original function's structure.

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 $f ( x ) = \frac { 3 x - 2 } { x + 5 }$