Inverses

Objectives - Find the inverse of a function algebraically - Determine if a relation is one-to-one. - Find the inverse of a function given its mapping diagram, input/output table, or equation

Inverses

-3

x y

11 -3

10 2

5 5

-1 4

x y

The inverse of a relation is the SWAPPING of input and output.

What is an inverse?

Is the given relation a function?

Is the inverse of the relation also a function?

This relation is a one-to-one function.

Inverse

Relation

When the inverse of a relation is a function, then we call the relation one-to-one.

One-to-One

Function: YES NO YES NO YES NOOne-to-One? YES NO YES NO YES NO

A relation with no repeating x-values is a function.A relation with no repeating y-values is one-to-one.

in other words...

Relation: {(3, 4), (-2, 4), (11, 7), (-1, 9), (-2, 8)}Inverse: {(4, 3), }Is the relation a function? One-to-One?

Just swap x and y!

Inverse from ordered pairs?

Step 1: If in function notation, rewrite with y instead of f(x).Step 2: Swap x and yStep 3: Solve for yStep 4: Write in inverse-function notation.

Finding an inversealgebraically.

Find the inverse of the function above.

To convert a temperature in Fahrenheit to Celsius, use the function:

Real world app

What does the inverse convert?

To convert a temperature in Fahrenheit to Celsius, use the function:

Real world app

Convert or

CFU in edio!

You should be able to... - Find the inverse of a function algebraically - Determine if a relation is one-to-one. - Find the inverse of a function given its mapping diagram, input/output table, or equation

Inverses