Find the inverse function $\mathrm { f } ^ { - 1 }$ of the function f.
-$$f ( x ) = 5 \tan ( 10 x - 9 )$$
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 5 \tan ^ { - 1 } ( 10 \mathrm { x } - 9 )$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 5 } \left[ \tan ^ { - 1 } \left( \frac { \mathrm { x } } { 10 } \right) + 9 \right]$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 10 } \left[ \tan ^ { - 1 } \left( \frac { \mathrm { x } } { 5 } \right) - 9 \right]$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 10 } \left[ \tan ^ { - 1 } \left( \frac { \mathrm { x } } { 5 } \right) + 9 \right]$

Question

Quizplus · Accepted Answer

To find the inverse function, you swap $x$ and $y$ and solve for $y$. Starting with $y = 5 \tan(10x - 9)$, swapping gives $x = 5 \tan(10y - 9)$. Solving for $y$ involves isolating the $\tan$ expression and then applying $\tan^{-1}$, leading to $y = \frac{1}{10} \left[ \tan^{-1}\left(\frac{x}{5}\right) + 9 \right]$.

Find the Inverse Function f−1\mathrm { f } ^ { - 1 }f−1

Find the Inverse Function $\mathrm { f } ^ { - 1 }$