The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. What are the restrictions on the domain of(u0v)(x)?

Answer: the restrictions on the domain of (u°v) (x) are  x ≠ 2 and which v(x) ≠ 0.

Justification:

1) the function (u ° v) (x) is u [ v(x) ], this is, you have to apply first the function v(x) whose argument is (x), and later the function u (v(x) ) whose argument is v(x).

2) So, the domain of the composed function  (u ° v) (x) has to take into account the values for which both functions are defined.

3) The domain excludes x = 2 because v(x) is not defined for x = 2.

4) And the domain must also exclude v(x) = 0 because u is not defined for v(x) = 0.

5) So, in conclusion,  the domain is all the real values except x = 2 and the x for which v(x) = 0.

Therefore the resctrictions are x ≠ 2 and v(x) ≠ 0