Question

Determine the function operations f ◦ g, f + g, and their domains for the functions f(x) = 22 - 16 and g(x) = 2 - 4:

A) Domain of each is all real numbers.
B) (f ◦ g)(x) = x² - 162 - 4; Domain of each is all real numbers except x = 4.
C) (f + g)(x) = 23 - 422 - 162 + 64; Domain of fog is all real numbers; the domain is all real numbers except x = 4.
D) (f ◦ g)(x) = 2 - 4; Domain of fog is all real numbers except x = 4; the domain of f + g is all real numbers.

Answer 1

The composite function f ◦ g(x) is equal to 6 and the sum of f(x) and g(x) is equal to 4. The domain of f ◦ g(x) is all real numbers except x = 4, while the domain of f + g is all real numbers.

Step-by-step explanation:

For function compositions, we use the notation f ◦ g(x) or (f ◦ g)(x) to represent the composite function. To find (f ◦ g)(x), we first substitute g(x) into the function f(x), and simplify the expression. In this case, f(x) = 22 - 16 and g(x) = 2 - 4.

So, (f ◦ g)(x) = f(g(x)) = f(2 - 4) = f(-2) = 22 - 16 = 6.

For addition of functions, we simply add the corresponding terms. In this case, f + g(x) = (22 - 16) + (2 - 4) = 6 - 2 = 4.

The domain of the composite function f ◦ g is all real numbers except x = 4, since dividing by zero is undefined. The domain of f + g is all real numbers.