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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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Presentation Transcript
slide1

Composition

of

Functions

By: Dr. Julia Arnold

slide2

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

slide3

That\'s nice!

But What Is It?

slide4

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.

slide5

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

slide6

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

slide7

An interesting fact is that

most of the time.

Let’s see if

this is the

case for

the

previous

example.

slide8

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

slide9

Those were easy!

My homework is

never that easy!

slide10

Okay!

I\'ll make it harder.

Let

and

Is that better?

slide11

Step 1

Write the f function

Step 2

Substitute g(x) for x

Step 3

Replace g(x) with

Step 4

Simplify

slide12

Your Turn!

Find:

When ready click your mouse.

The answer is:

A)

Move your mouse over

the correct answer.

B)

slide13

Your Turn Again!

Find:

The answer is:

When ready click your mouse.

A)

Move your mouse over

the correct answer.

B)

slide14

Once More! Come On!

Find:

The answer is:

When ready click your mouse.

A)

Move your mouse over

the correct answer.

B)

slide16

Practice makes perfect!

Do the practice problems following

This module in your module section

Of Blackboard. Check your work using

This live math page.

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