Question

Using interval notation, the domain off is [- 3, 5] and the domain of g is [- 2, 7] . On what domain is f defined

Answer 1

Note: I am assuming you mean ''on what domain is f+g is defined''.

Answer:

We conclude that

• Dom(f+g) = [-2, 5]

Explanation:

Given the domain of f

[-3, 5]

Given the domain of g

[-2, 7]

• The domain of a composition f+g would include the intersection of both domains.

In other words, the domain of a composition f+g includes all the inputs of x-values that are in the domain of both functions i.e. f and g.

so

Domain of f = [-3, 5]

The x-values lie in the domain of f interval are:

x = -3, -2, 1, 0, 1, 2, 3, 4, 5

Domain of g = [-2, 7]

The x-values lie in the domain of g interval are:

x = -2, 1, 0, 1, 2, 3, 4, 5, 6, 7

Therefore, the common x-values in both f and g would be:

-2, 1, 0, 1, 2, 3, 4, 5

Thus, we conclude that

• Dom(f+g) = [-2, 5]