Find the inverse function 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 $f^{-1}(x)$, we swap $x$ and $y$ in the original function and solve for $y$. Starting with $y = 5\tan(10x - 9)$, we swap to get $x = 5\tan(10y - 9)$. Solving for $y$, we isolate the tangent function and apply the inverse tangent to both sides, leading to $y = \frac{1}{10}[\tan^{-1}(\frac{x}{5}) + 9]$, which matches choice D.

Find the Inverse Function F-1 of the Function F f(x)=5tan⁡(10x−9)f ( x ) = 5 \tan ( 10 x - 9 )f(x)=5tan(10x−9)

Find the Inverse Function F-1 of the Function F $f ( x ) = 5 \tan ( 10 x - 9 )$