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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

of

Functions

By: Dr. Julia Arnold


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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


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That's nice!

But What Is It?


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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.


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For example: substitution. In fact

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


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g( substitution. In factx) = 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


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An interesting fact is that substitution. In fact

most of the time.

Let’s see if

this is the

case for

the

previous

example.


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f( substitution. In factx) = 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


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Those were easy! substitution. In fact

My homework is

never that easy!


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Okay! substitution. In fact

I'll make it harder.

Let

and

Is that better?


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Step 1 substitution. In fact

Write the f function

Step 2

Substitute g(x) for x

Step 3

Replace g(x) with

Step 4

Simplify


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Your Turn! substitution. In fact

Find:

When ready click your mouse.

The answer is:

A)

Move your mouse over

the correct answer.

B)


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Your Turn Again! substitution. In fact

Find:

The answer is:

When ready click your mouse.

A)

Move your mouse over

the correct answer.

B)


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Once More! Come On! substitution. In fact

Find:

The answer is:

When ready click your mouse.

A)

Move your mouse over

the correct answer.

B)


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Ans. A for the previous example substitution. In fact

Was actually

A)


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Practice makes perfect! substitution. In fact

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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