The noun purview is used to refer to the range of operation, authority, or control of something or of someone in a particular function. Purview is most commonly used in locating responsibility or oversight for specified activities or projects. For example, in the U.S. government, disaster readiness falls under the purview of the Department of Homeland Security. You may also encounter this term used in reference to a particular range of insight or understanding. The noun scope, though also indicating extent, does not on its own suggest authority or responsibility. An investigation of wide scope is simply one that is far reaching.
The surefooted adjective unequivocal describes things that are unambiguous or have only one possible meaning or interpretation: unequivocal proof is proof that cannot be refuted or misinterpreted. Unequivocal also describes things that are absolute or not subject to conditions or exceptions. To have someone’s unequivocal support is to know that they will be there for you no matter what, no strings attached.
Something that is ancillary is additional or supplemental. The ancillary costs of something are those “extra” expenditures beyond the sticker price of a product or service. This sense of ancillary is closest to extra when the latter is used to refer to things that are additional or go beyond what is expected. But ancillary suggests a more defined relationship than extra, usually indicating a subordinate or subsidiary position. Used in a medical context, ancillary feels quite far from extra: in this context ancillary describes services or staff that provide essential support, as in a hospital. So remember, context is key!