Algebra II Recipe: Operations with Functions

A. Operations with Functions

Given f(x) = 3x  and  g(x) = -x - 5

1. Addition:         f(x) + g(x) = 3x + (x - 5) = 4x - 5
2. Subtraction:    f(x) - g(x) = 3x - (x - 5) = 2x + 5
3. Multiplication:  f(x) • f(g) = 3x(x - 5) = 3x² - 15x
4. Quotient:        f(x) ÷ g(x) = (3x)/(x - 5), x ≠ 5

B. Evaluating Composite Functions

1. Given two functions f(x) and g(x), a composite function is written g[f(x)] and is read "g of f of x"
2. The "f" and "g" are simply to name the function.

Given f(x) = -3x  and g(x) = x + 2