Question

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 ? u(x) 0 and v(x) 2 x 0 and x cannot be any value for which u(x) 2 x 2 and x cannot be any value for which v(x) 0 u(x) 2 and v(x) 0

Answer 1

The answer is C on edge.

Answer 2

Third option

x ≠2 and x cannot be any value for which v(x) = 0

Explanation:

In this problem we are asked to find the domain of the function

`(UoV)(x)`

We know that
`(UoV)(x) = U(V(x))`.

We know that:

Domain of U(x) is all real numbers except x = 0

Domain of V(x) is all real numbers except x = 2.

Then the domain of the composite function U(V (x)) is:

all real numbers except x = 2. (since x = 2 does not belong to the domain of V(x) and all values of x for which V(x) = 0 (since x = 0 does not belong to the domain of U(x))

Finally the domain of
`(UoV)(x)`) is:

`x \\eq 2` and
`V(x) \\eq 0`