Question

How do you write the equation for the inverse of the function `y=cos 2x`?

Answer 1

`x=arccos(y)/2` for `y in [-1,+1]`

Explanation:

Provided `2x in [0,pi]`
`color(white)("XXX")`which implies that `x in [0,pi/2]`
`color(white)("XXX")`and that `y in [-1,+1]`
then
`2x=arccos(cos(2x))`
or
`2x=arccos(y)`

and therefore
`x=arccos(y)/2` provided `y in [-1,+1]`