Find the inverse function $\mathrm { f } ^ { - 1 }$ of the function f.
-$$f ( x ) = \cos ( x - 9 ) - 5$$
A) $f ^ { - 1 } ( x ) = \cos ^ { - 1 } ( x - 5 ) - 9$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \cos ^ { - 1 } ( \mathrm { x } + 5 ) + 9$
C) $f ^ { - 1 } ( x ) = \cos ^ { - 1 } ( x + 9 ) + 5$
D) $f ^ { - 1 } ( x ) = \cos ^ { - 1 } ( x - 9 ) - 5$

Question

Quizplus · Accepted Answer

To find the inverse function, we swap $x$ and $y$ and solve for $y$. Starting with $y = \cos(x - 9) - 5$, we swap to get $x = \cos(y - 9) - 5$, then solve for $y$. Adding 5 to both sides gives $x + 5 = \cos(y - 9)$. Taking the inverse cosine of both sides yields $y - 9 = \cos^{-1}(x + 5)$, and finally, adding 9 to both sides gives $y = \cos^{-1}(x + 5) + 9$, which matches choice B.

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

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