we are given
[tex]y=cos(2x)[/tex]
Since, we have to find inverse function
so, we will use following steps
step-1:
Set y=f(x)
It is already there
step-2:
Switch x and y
[tex]x=cos(2y)[/tex]
step-3:
Solve for y
[tex]x=cos(2y)[/tex]
we can take cos^-1 both sides
[tex]cos^{-1}(x)=cos^{-1}(cos(2y))[/tex]
now, we can simplify it
[tex]cos^{-1}(x)=2y[/tex]
Divide both sides by 2
[tex]y=\frac{cos^{-1}(x)}{2}[/tex]
so, option-D........Answer
