Section 1.4 Combinations of Functions

The domain of an Arithmetic combination of functions f and g consists of all real numbers that are common to the domains of f and g. In the case of the quotient f(x)/g(x) - g(x) ≠ 0.

1. Sum: (f + g)(x) = f(x) + g(x)

2. Difference: (f – g)(x) = f(x) – g(x)

3. Product: (fg)(x) = f(x) ∙ g(x)

4. Quotient: (f/g)(x) = f(x)/g(x), g(x) ≠ 0

ex. (f + g)(x) = f(x) + g(x)

= (2x + 1) + (x² + 2x – 1)

= x² + 4x

Composition of Functions

(f ○ g)(x) = f(g(x))

ex. f(x) = x + 2 g(x) = 4 – x²

(f ○ g)(x) = f(g(x))

= f(4 – x²)

= (4 – x²) + 2

= –x² + 6