Composition of Functions

Hey everyone,

Today in the class we learned the composition of functions and for the homework we get the Compositions of Functions worksheet.Compositions of functions is represented by (f∘ g)(x).It means the range of f is domain of g.To make it simple wherever you
 see " x" in  function f(x) substitute the function g(x).

Here's one example :

Example.1

f(x)=3x²-5x

g(x)=2x-3

Find (f ∘ g)(x)

Solution:Substitute g(x) wherever you see an x in the function of f(x)

3(2x-3)²-5(2x-3)

Now foil (2x-3)²

3(4x²-12x+9)-5(2x-3)

12x²-36x+27-10x+15

Combine like terms.

12x²-46t+42


Example no. 2

g(a)=a³ -4a²

f(a)=-4a-1

Find (g∘f)(a)

Solution:

Step 1:Where you see "a " in function g(a) substitute the function f(x) .

(-4a-1)³-4(-4a-1)²


Step 2 :Foil it

Formula for (a+b)³ is a³+3a²b+3ab²+b³

(a+b)² is a²+2ab+b²

a=-4a and b = -1


Substitute into the formula


(-4a)³+3(-4a)²(-1)+3(-4a)(-1)²+(-1)³-4((-4a)²+2(-4a)(-1)+(-1)²)
-64a³-48a²-12a-1-4(16a²+8a+1)
-64a³-48a²-12a-1-64a²-32a-4


Step 3 :Combine like terms


-64a³-112a²-44a-5


Just a reminder to everyone the we have a test on Analytic Geometry tomorrow.Make sure you guys do the review for the test that we got for Analytic Geometry.Don't forget  to study.Good Luck to everyone !!!


and...................


One tip for tomorrow's test
Do every solution step by step and use the brackets every time and check for the signs too even if you are very good in handling those signs. It is pretty easy to make mistake in substitution and elimination problems.It is the last test so do your best.


Our Project is due tomorrow.


Have a good evening.See you all tomorrow.