Find the inverse function f-1 of the function f.
-$$f ( x ) = - 4 \cos ( 10 x + 7 )$$
A) $f ^ { - 1 } ( x ) = - 4 \cos ^ { - 1 } ( 10 x + 7 )$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 4 } \left[ \cos ^ { - 1 } \left( \frac { \mathrm { x } } { 10 } \right) - 7 \right]$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 10 } \left[ \cos ^ { - 1 } \left( \frac { \mathrm { x } } { 4 } \right) - 7 \right]$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 1 } { 10 } \left[ \cos ^ { - 1 } \left( \frac { \mathrm { x } } { 4 } \right) + 7 \right]$

Question

Quizplus · Accepted Answer

To find the inverse, solve for x: $ y = -4 \cos(10x + 7) $. Rearrange to get $\cos(10x + 7) = -\frac{y}{4}$. Then, $10x + 7 = \cos^{-1}(-\frac{y}{4})$. Solve for x: $x = \frac{1}{10}[\cos^{-1}(-\frac{y}{4}) - 7]$. Replace y with x for the inverse: $f^{-1}(x) = \frac{1}{10}[\cos^{-1}(-\frac{x}{4}) - 7]$. Since $\cos^{-1}(-z) = \pi - \cos^{-1}(z)$, the correct form is $f^{-1}(x) = \frac{1}{10}[\cos^{-1}(\frac{x}{4}) - 7]$.

Find the Inverse Function F-1 of the Function F f(x)=−4cos⁡(10x+7)f ( x ) = - 4 \cos ( 10 x + 7 )f(x)=−4cos(10x+7)

Find the Inverse Function F-1 of the Function F $f ( x ) = - 4 \cos ( 10 x + 7 )$