Question

Find each of the following functions and determine the domain of each of them:

(f + g) (x)
(f - g) (x)
(f * g) (x)
(f / g) (x)
(f o g) (x)

Answer 1

To find each of the following functions and determine their domain, we need to start with the individual functions f(x) and g(x) and then perform the specified operations.

Step-by-step explanation:

To find each of the following functions and determine their domain, we need to start with the individual functions f(x) and g(x) and then perform the specified operations. Let's assume f(x) = a and g(x) = b for simplicity.

1. (f + g)(x) = a + b. The domain is the set of all real numbers.
2. (f - g)(x) = a - b. The domain is the set of all real numbers.
3. (f * g)(x) = a * b. The domain is the set of all real numbers.
4. (f / g)(x) = a / b, where b is not equal to 0. The domain is the set of all real numbers except 0.
5. (f o g)(x) = f(g(x)), which means substituting g(x) into f(x). The resulting function and its domain depend on the specific functions f(x) and g(x) given.