1. 3.5 Operations on Functions
Sum & Difference: If f & g are functions, then their sum and difference can be defined by the following rules.
Sum: (f + g)(x) Difference: (f - g)(x)
Ex. 1 Let f(x) = 2x2 + 7x and g(x) = 2x – 3.
Find (f + g)(x) & the domain.
b) Find (f – g)(x) & the domain.

2. Ex. 2 Let f(x) = 3x + 2 and g(x) = x3 + 1
Find (g – f)(x) and the domain.
Find (f + g)(-1).
c) Find (f – g)(2).

3. Product & Quotient: If f & g are functions, then the product and quotient can be defined with the following rules.
Product: (fg)(x) Quotient: (x) Ex. 3 Let f(x) = -4x + 3 & g(x) = x2 a) Find (fg) and the domain.

4. b) Find (x) and the domain. c) Find (x) and the domain.

5. Composite Functions: To take the composition of a function is to use the output of one function as the input of another.
If f and g are functions, then the composite function of f and g is: (g o f)(x) = g(f(x)) **Functions are applied from right to left, which means, evaluate f, get an answer and plug that answer into g.**

6. Ex. 4 Let f(x) = x2-1 and g(x) =
a) Find (g o f)(3) b) Find (f o g)(1)

7. Domain of g o f: The domain of g o f is the set of x’s that satisfy both f(x) and g(x).
Ex. 5 Let f(x) = -3x + 2 and g(x) = x3.
Find gof(x) & its domain.
b) Find fo g(x) & its domain.