Operations on Functions Lesson 3.5

Sums and Differences of Functions If f(x) = 3x + 7 and g(x) = x 2 – 5 then, h(x) = f(x) + g(x) = 3x (x 2 – 5) So, h(x) = x 2 + 3x – 2 Now, if h(x) = f(x) – g(x), then 3x + 7 – (x 2 – 5) = -x 2 + 3x + 12

Example

Products and Quotients If f(x) = 3x and g(x) = 4, then f(x)g(x) = 4(3x 2 + 7) = 12x

Composition of Functions If f and g are functions, then the composite function of f and g is (g◦f)(x) = g(f(x)) The expression g ◦ f is read g circle f or f followed by g. The functions are applied right to left.

Examples

Domain of g ◦ f Let f and g be functions. The domain of g ◦ f is the set of all real numbers x such that –x is in the domain of f –f(x) is in the domain of g

Example

Writing a Function as a Composite

Applications