Question

Find the inverse function of F(x) = 2arccosx. F-1(x) = ____

Answer 1

ANSWER

C.

${f}^{ - 1} (x) = \cos( \frac{x}{2} )$

EXPLANATION

The given function is

$f(x) = 2 \arccos(x)$

Let

$y= 2 \arccos(x)$

Interchange x and y.

$x= 2 \arccos(y)$

Divide both sides by 2.

$\frac{x}{2} = \arccos(y)$

We take cosines to get,

$\cos( \frac{x}{2} ) = y$

${f}^{ - 1} (x) = \cos( \frac{x}{2} )$