Example of function composition, Algebra

Given f(x)= 2+3x-x2 and g(x) =2x-1 evaluate  ( fg ) ( x ) , (fog)(x) and (gof )(x)


These are the similar functions that we utilized in the first set of instances and we've already done this part there hence we won't redo all the work here.  This is here only here to demonstrate the point that function composition is not function multiplication.

Following is the multiplication of these two functions.

( fg ) ( x ) = -2 x3 + 7 x2 + x - 2

 (b) Now, for the purpose of function composition all you have to remember is that we are going to plug the second function tabulated into the first function listed.  If you can recall that you must always be capable to write down the fundamental formula for the composition.

Here is this function composition.

                ( f o g ) ( x ) = f [g ( x )]

                                     = f [2x -1]

                                       = 2+ 3( 2 x -1) - ( 2 x -1)2

                                       = 2 + 6 x - 3 - (4 x2 - 4 x + 1)

= -1 + 6 x - 4 x2 + 4 x -1

= -4 x2 + 10 x - 2

Notice that it is very different from the multiplication! Remember that function composition is NOT function multiplication.

c) We'll not put in the detail in this part as it works really the same as the previous part.

                ( g o f ) ( x ) = g [f ( x )]

                                      = g[2+3x-x2]

                                      = 2(2+3x-x2)-1



Notice that it is NOT the similar answer as that from the second part.  In most of the cases the order in which we do the function composition will give distinct answers.

Some facts are important enough to make again.  First, function composition is different from function multiplication.  Second, the order of function composition is important. In most of the case we will get distinct answers with a different order. Note though, that there are times when we will get the same answer regardless of the order.

Posted Date: 4/8/2013 1:20:04 AM | Location : United States

Related Discussions:- Example of function composition, Assignment Help, Ask Question on Example of function composition, Get Answer, Expert's Help, Example of function composition Discussions

Write discussion on Example of function composition
Your posts are moderated
Related Questions
find the x-and y-intercepts ofline represented by the equatics with stepy by step instructions and explained in words

how do you make the fraction 17 5ths a mixed number?????

2 adults for 10 children and 3 adults for 12 children

I have an algebra test tomorrow and still don''t understand how to simplify and solve radicals

Example    Solve each of the following systems of equations.              5x + 4 y = 1              3x - 6 y = 2 Solution It is the system in the previous examples wh

Find an equation of the line containing each pair of points. Write your final answer in slope-intercept form. (-2,0) and (0,-7)

Which shows the quadratic function f(x) = 2(x - 4)2 - 7 in standard form?

General problems for homework