Question

Find the domain of  `f(x) =2cos^-1 2x+sin^-1x.`

Answer 1

For `2cos^-1 2x` to be defined.

`-1<=2x<=1`

`=>-1/2<=x<=1/2`  .....(i)

For `sin^-1x` to be defined.

`-1<=x<=1`      .....(ii)

Domain of `f(x) = [-1/2,1/2]cap[-1,1]`

`=[-1/2,1/2]`.