Find the inverse function f-1 of the function f.
-$$f ( x ) = 3 \sin x - 2$$
A) $f ^ { - 1 } ( x ) = 3 \sin ^ { - 1 } x - 2$
B) $f ^ { - 1 } ( x ) = \sin ^ { - 1 } \left( \frac { x + 2 } { 3 } \right)$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \cos \left( \frac { \mathrm { x } + 2 } { 3 } \right)$
D) $f ^ { - 1 } ( x ) = \sin ^ { - 1 } \left( \frac { x + 3 } { 2 } \right)$

Question

Quizplus · Accepted Answer

To find the inverse function, solve the equation $y = 3\sin x - 2$ for $x$. Rearranging, we get $\sin x = \frac{y + 2}{3}$. Taking the inverse sine of both sides gives $x = \sin^{-1}\left(\frac{y + 2}{3}\right)$, which means $f^{-1}(x) = \sin^{-1}\left(\frac{x + 2}{3}\right)$.

Find the Inverse Function F-1 of the Function F f(x)=3sin⁡x−2f ( x ) = 3 \sin x - 2f(x)=3sinx−2

Find the Inverse Function F-1 of the Function F $f ( x ) = 3 \sin x - 2$