The function fx=sec-1xx-x, where [x] denotes the greatest integer less than or equal to x, is defined for all x∈

The function sec-1x is defined for all x∈R--1,1 and the function 1x-x is defined for all x∈R-zSo, the given function is defined for all x∈R--1,1∪n|n∈Z.