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 (uv)(x)?

Answer 1

The restriction on the domain of the product function (uv)(x) is:

All the real numbers except 0 and 2.

Explanation:

We are given two function u and v and we are asked to find the domain of the composite function.

(uv)(x)

Since, we know that the product function (uv)(x) could also be represented as:

(uv)(x)=u(x).v(x)

So for the product function to exist each of the function u(x) and v(x) must also exist i.e. the function u and v are well defined.

Hence, the domain of the product function is:

All the real numbers except 0 and 2.

Answer 2

The domain of (uv)(x) is the set of all real values except 0 and 2.