Course:
For Pre-calculus students
Created by Kameswari Tekumalla for Synergy Project (March 6th)
Uses Weblinks produced by Bob Mathews, Houghton Mifflin, CoolMath
Background:
A function is a rule or procedure for producing a result that may depend on the value of some input. The important aspect of a function is that there is a unique output for each possible input. It is possible to have variables related in a way that does not determine one in terms of the other, but such relations are not functions. To have a better view of functions visit a nice Introduction to the function concept that is provided at the "Cool Math" site maintained by an instructor at a community college in California.
Just as the operations of addition, subtraction, multiplication, and division can combine two real numbers to form other real numbers, so too two functions can be combined to create new functions. In addition to combining functions algebraically (e.g., by adding or multiplying their output values), we also can take the output of one and feed it in as the input to another (for example, to produce the square of sin (x)). This process is called COMPOSITION of functions. To learn more about them, click on the link Algebra of functions. To see the effects graphically, visit the web site Graphical Utility, and for composition of functions, click on Tool for composition of functions. Composite functions are so common that we usually don't think to label them as composite functions. However, they arise any time a change in one quantity produces a change in another, which in turn, produces a change in a third quantity. To see more examples, Click here. To see whether you understand the concepts, take Online Testing.
QUESTIONS:
Q1. Suppose the functions f and g are given in numerical forms:
|
X |
-2 |
-1 |
0 |
1 |
2 |
3 |
|
F (x) |
8 |
2 |
7 |
-1 |
-5 |
-3 |
|
G (x) |
-1 |
-5 |
-11 |
7 |
8 |
9 |
Find the numerical (table) forms of (f + g)(x), (f-g)(x), (f ·g)(x), (f/g)(x)
Q2. Give an example of two functions f and g such that fog (x) =g of (x).