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# 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