Question

For the functions f(x) = 2x + 1 and g(x) = √(x + 3), determine (f + g)(x) and its domain.

a) (f + g)(x) = 2x + 1 + √(x + 3), Domain: All real numbers
b) (f + g)(x) = 2x + 1 - √(x + 3), Domain: x ≥ -3
c) (f + g)(x) = 3x + √(x + 3), Domain: x ≥ -3
d) (f + g)(x) = x + 4, Domain: All real numbers

Answer 1

To find (f + g)(x), add the functions f(x) and g(x) together. The domain of (f + g)(x) is all real numbers.

Step-by-step explanation:

To find (f + g)(x), we simply add the functions f(x) and g(x) together.

(f + g)(x) = (2x + 1) + √(x + 3)

The domain of (f + g)(x) is the intersection of the domains of f(x) and g(x). Since f(x) and g(x) are defined for all real numbers, the domain of (f + g)(x) is also all real numbers.