# Operations and Functions

## 1.4 Operations and Functions

**Let f(x) be a function with domain A.
Let g(x) be a function with domain B.**

**Methods for combining functions:**

**1. Sum** ( f + g)(x) = f (x) + g(x) (domain of f + g
is A∩ B )

**2. Difference** ( f - g)(x) = f (x) - g(x) (domain of
f - g is A∩ B )

**3. Product** ( fg)(x) = f (x)g(x) (domain of fg is A∩
B )

**4. Quotient**

**5. Composition **
**(domain we will discuss later in this section)**

**Example 1:** Let f (x) = 2x^2 - 3x +1 and let g(x) =
5x - 3 . Find and state the domain of the

following functions:

**Example 2:** Let Find:

(d) the domain of f/g.

**Composition of Functions:**

There is one more type of function combination we will
see, it is called the

COMPOSITION of two functions and is denoted .

By definition: ()(x) = f (g(x)) This is often
read as “f of g of x”. What you do to

evaluate this composition function at a number x is evaluate g at x, then plug
that number

into f.

**Example 3:** Let f (x) = x^2 + x -1 and g(x) = 1- 2x
. Find:

The domain of is
or To find the domain of
, first compose the

functions and find the rule for f (g(x)) . Then find the domain of this new
function

f(g(x)) . Also find the domain of g(x) (the “inside” function). Combine these
and you

will have the domain of .

**Example 4:** Let Find:

(c) The domain of