Download Function Operations

NOTES: Function Operations
Name ________________________ Per. ______
To ADD polynomials,
Ignore the parentheses and combine like terms!
(4 y  7)  (3 y  2)
(a 2  2a)  (6a 2  10a)  (5a  1)
To SUBTRACT polynomials,
Distribute the subtraction sign to each term inside the second parentheses, then
combine like terms!
(3x  2)  (4 x  9)
(5z 2  12 z )  (4 z  8)
To MULTIPLY binomials, use “FOIL”
**When multiplying two polynomials, multiply every term in the first polynomial by
every term in the second polynomial, and add the products together.
 2a  53a  4
(5x  2)( 4 x 2  3x  1)
Composition of Functions!
The notation used for the composition of functions looks like this: (f  g)(x).
The composition of the function f with g is defined as follows: (f  g)(x) = f(g(x)), notice that
in this case, the function g is inside of the function f
To find the composition of two functions:
Step 1: Rewrite the composition in a different form if needed. For example,
the composition (f og)(x) needs to rewritten as f(g(x)).
Step 2: Replace each occurrence of x found in the outside function with
the inside function. For example, in the composition of (f  g)(x) = f(g(x)), we need to replace
each x found in f(x), the outside function, with g(x), the inside function.
Step 3: Simplify the answer.
Given:
Evaluate
f(2)
f ( x)  3x  2
g(x) = 4x 2
f(g(x))
h(x) = x  6
(f  g)(x)
(h  f) (x)
Practice!
Suppose f(x) = 2x  4 and g(x) = x  6 . Complete the following. Simplify completely.
1.
f(x) + g(x)
2.
f(x) – g(x)
3.
f(g(2))
4.
f(x)  g(x)
5.
f(g(x))
6.
(g ◦ f) (x)