Answer: R minus the open interval (-1,1).
- A All real numbers without any restriction
- B The closed interval from -1 to 1
- C R minus the open interval (-1,1)
- D Positive real numbers greater than zero
Correct answer: C. R minus the open interval (-1,1)
Explanation: sec-1 x is defined for |x| >= 1, i.e., the domain excludes the open interval (-1,1).
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.