ANSWER
C.
[tex]{f}^{ - 1} (x) = \cos( \frac{x}{2} ) [/tex]
EXPLANATION
The given function is
[tex]f(x) = 2 \arccos(x)[/tex]
Let
[tex]y= 2 \arccos(x)[/tex]
Interchange x and y.
[tex]x= 2 \arccos(y)[/tex]
Divide both sides by 2.
[tex] \frac{x}{2} = \arccos(y)[/tex]
We take cosines to get,
[tex] \cos( \frac{x}{2} ) = y[/tex]
[tex] {f}^{ - 1} (x) = \cos( \frac{x}{2} ) [/tex]
