Find the domain of `sec^(-1)(2x+1)`

Explanation

The domain of `sec^{-1} x` is `(-infty,-1] cup[1, infty)`

Therefore `sec ^{-1}(2 x+1)` is meaningful if

`2x+1>=1` or `2x+1<=1`

`2x>=0` or `2x<=-2`

`x>=0` or `x<=-1`

`x(-infty,-1]cup[0,infty)`

Hence the domain of `sec ^{-1}(2 x+1)` is `(-infty,-1] cup[0, infty)`