Creating New Functions out of Old Ones
Written by Frances E.M. Alvarado
January 28, 2006
Okay now we are going to create new functions by combining two or more
functions that are known to us. Don’t panic most of this will look familiar to
you.
First we are going to find new functions by Adding, Subtracting, Multiplying,
and Dividing 2 functions.
Adding, Subtracting, Multiplying, and Dividing 2 or more Functions
The following example represents how a question may look on a test paper.
Example : Using
2x3xf
and
2xx3xg
2
and
12xxh
Find the following:
1.)
xgf
________________
2.)
xgf
________________
3.)
xgf
__________________
4.)
x
g
f
________________
5.)
xhgf
_____________
Now for how to work them out – basically this is another game of notation.
You need to understand what the problem is asking you to do. So we will first
work with a known value of x and then figure out what has truly been asked.
(well that’s what I am hoping for anyway)
SO let us begin with problem number 1 – the addition of two
functions.
2x3xf
and
2xx3xg
2
Find
xgf
means to find
xgxf
which means what?????
Okay let’s go into an example with some values for x first. Let’s explore
1.)
3gf
3g3f
= ????
well remember what f(3) means??? It means go find the y value that works in
the f-function when x = 3
