Composition

1 / 16

Composition - PowerPoint PPT Presentation

Composition. of Functions. By: Dr. Julia Arnold. Composition is a binary operation like addition , subtraction, multiplication and division are binary operations. (meaning they operate on two elements). f-g. f+g. f g. The composition symbol is: . Thus . That's nice!. But What Is It?.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about 'Composition' - Antony

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Composition

of

Functions

By: Dr. Julia Arnold

Composition is a binary operation like addition , subtraction, multiplication and division are binary operations. (meaning they operate on two elements)

f-g

f+g

fg

The composition symbol is:

Thus

That's nice!

But What Is It?

The easiest way to describe composition is to say it is like substitution. In fact

Read f of g of x which means substitute g(x) for x in the f(x) expression.

For example:

Suppose

f(x)= 2x + 3, and

g(x) = 8 - x

Then

Means substitute the g function for

x in the f function… like this

f(x)= 2x + 3

f(g(x) )= 2 g(x) + 3

g(x) = 8 - x

f(x)= 2x + 3, and

f(x)= 2x + 3

f(g(x) )= 2 g(x) + 3

Now

substitute

what

g equals

for g(x)

f(8 - x)= 2 (8 - x) + 3

= 16 - 2x + 3

= 19 - 2x

So, = 19 - 2x

An interesting fact is that

most of the time.

Let’s see if

this is the

case for

the

previous

example.

f(x) = 2x + 3, and

g(x) = 8 - x

Thus we will substitute f into g.

g(x) = 8 - x

g(f(x) ) = 8 - f(x)

Now

substitute

what f(x) is:

g(2x + 3) = 8 - (2x + 3)

= 8 - 2x - 3

= 5 - 2x

Those were easy!

My homework is

never that easy!

Okay!

I'll make it harder.

Let

and

Is that better?

Step 1

Write the f function

Step 2

Substitute g(x) for x

Step 3

Replace g(x) with

Step 4

Simplify

Find:

A)

B)

Find:

A)

B)

Once More! Come On!

Find:

A)