Find the inverse function $\mathrm { f } ^ { - 1 }$ of the function f.
-$$f ( x ) = 7 \cos x + 4$$
A) $f ^ { - 1 } ( x ) = 7 \cos ^ { - 1 } x + 4$
B) $f ^ { - 1 } ( x ) = \cos ^ { - 1 } \left( \frac { x + 4 } { 7 } \right)$
C) $f ^ { - 1 } ( x ) = \sin \left( \frac { x - 4 } { 7 } \right)$
D) $f ^ { - 1 } ( x ) = \cos ^ { - 1 } \left( \frac { x - 4 } { 7 } \right)$

Question

Quizplus · Accepted Answer

To find the inverse function, we first replace $f(x)$ with $y$, giving us $y = 7\cos(x) + 4$. Then, we solve for $x$ in terms of $y$. Subtract 4 from both sides to get $y - 4 = 7\cos(x)$, then divide by 7 to isolate $\cos(x)$, resulting in $\cos(x) = \frac{y - 4}{7}$. Finally, apply the inverse cosine ($\cos^{-1}$) to both sides to solve for $x$, yielding $x = \cos^{-1}\left(\frac{y - 4}{7}\right)$. Replace $y$ with $f^{-1}(x)$ to get the inverse function $f^{-1}(x) = \cos^{-1}\left(\frac{x - 4}{7}\right)$.

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

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