Inverses
HS Math
Created on September 10, 2024
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Transcript
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