Answer: It excludes both 0 and pi as open endpoints.
- A 0, since the range starts strictly above zero
- B pi/2, a value that cot-1 x does not actually reach
- C pi, a value that cot-1 x does not actually attain
- D It excludes both 0 and pi as open endpoints
Correct answer: D. It excludes both 0 and pi as open endpoints
Explanation: The principal value range of cot-1 x is the open interval (0, pi), so both endpoints 0 and pi are excluded.
The graph of sin⁻¹x is confined to a narrow domain [-1,1] (since sine itself only takes values in that range) and range [-π/2,π/2] (the principal value branch chosen to make sine one-one and invertible there).
Concept context
Restricting trig functions to make them invertible, the principal value branches of sin-inverse, cos-inverse, tan-inverse, and friends, and the key identities relating them.