Final answer:
The restrictions on the domain of (u \circ v)(x) are that x cannot be any value making v(x) = 2, and also x itself cannot be 0, as u(x) is undefined at 0.
Step-by-step explanation:
The restrictions on the domain of the composition function (u \circ v)(x) depend on the restrictions of both u(x) and v(x). Since u(x) is not defined at x=0 and v(x) is not defined at x=2, we first recognize that x cannot be such that v(x) = 2 because u(2) is not defined. Similarly, x also cannot be a value that makes u(x) = 0, since u(x) is not defined at 0. Therefore, to find the restrictions on the domain of (u \circ v)(x), one must find the values of x for which v(x) equals to 2 and exclude those, as well as ensuring that v(x) itself is not zero because u(0) is undefined.
The correct option that describes the restrictions on the domain of (u \circ v)(x) is 'b. X \\eq 0 and x cannot be any value for which v(x) = 2'.