Operations with FunctionsSection 2.4

Sum Difference Product Quotient Composition

Types of Operations

Sum: (f+g)(x)=f(x)+g(x) Difference: (f-g)(x)=f(x)-g(x) Product: (f*g)(x)=f(x)*g(x) Quotient: (f/g)(x)=f(x)/g(x)

Math Mumbo Jumbo

Add or subtract like terms Watch out for negative signs Watch your parentheses

Basically….

Let f(x)=5x2 -2x+3 and g(x)=4x2 +7x-5

Find f +g and f-g

Example 1

Let f(x)=5x2 -2x+3 and g(x)=4x2 +7x-5

Find f *g and f/g

Example 2

Try these: Let f(x)=-7x2+12x-2.5 and g(x)=7x2-

5 Find f+g and f-g Find g-f

Let f(x)=3x2+1 and g(x)=5x-2Find f*g and f/g

In your groups

Worksheet

What on earth does that mean? When you apply a function rule on the

result of another function rule, you compose the functions

In other words, where there is an x in the first function, you actually plug the entire second function in it.

Composition of Functions

Do not confuse the symbol for composition, open dot, with the symbol for multiplication (closed dot)

f

Let Find f

Example

Let and g(x)=3x+1Find f

Example 2

Worksheet

Inverses of FunctionsDomains and RangesHorizontal Line Test

Relating Composition to Inverses

Helps us with inverses, by being an easy way to identify them

Why learn composition?

Basically an inverse switches your x and y coordinates

A normal ordered pair reads (x,y) while an inverse reads (y,x)

What is an inverse?

Find the inverse of the relation below {(1,2), (2,4), (3,6), (4,8)}

Example

The domain of an inverse is the range of the original function

The range of an inverse is the domain of the original

Domain and range flip just as the x and y flip for an inverse.

Domain and Range of an inverse

Find the inverse of the relation below {(1,2), (2,4), (3,6), (4,8)} Find the domain of the relation Find the range of the relation

Example

1. Interchange x and y 2. Solve for y. Example: y=3x-2

Solving an equation for an inverse

y=.5x-3

Find the inverse

Use the horizontal line test The inverse of a function is a function if and

only if every horizontal line intersects the graph of the given function at no more than one point

Look at the original graph, If it passes the vertical line test, the graph is a

function If it also passes the horizontal line test, the

inverse of the graph will also be a function

Is the inverse a function?

If a function has an inverse that is also a function, then the function is one to one

If f and g are functions and (f

Example: Show that f(x)=7x-2 and g(x)=1/7x+2/7 are inverses of one another

Composition of a function and its inverse

Show that f(x)=-5x+7 and g(x)=-1/5x+7/5 are inverses of one another

Graphic organizer

Summary