# Composition - PowerPoint PPT Presentation

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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?.

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Composition

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#### 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)

B)

Ans. A for the previous example

Was actually

A)

Practice makes perfect!

Do the practice problems following

This module in your module section

Of Blackboard. Check your work using

This live math page.