Question

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

a.) 1/2 cos(x)
b.) 2 cos(x)
c.) cos (1/2 x)
d.) cos (2x)

Answer 1

C.

`{f}^( - 1) (x) = \cos( (x)/(2) )`

Step-by-step 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.

`(x)/(2) = \arccos(y)`

We take cosines to get,

`\cos( (x)/(2) ) = y`

`{f}^( - 1) (x) = \cos( (x)/(2) )`