AA3-0 Inverse functions investigation

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We already know that some operations "undo" other operations. We call these inverse operations. Match the operations below with their inverse operation:

Draggable item		Corresponding Item
square		subtract
square root		divide
multiply		add
divide		multiply
subtract		square root
add		square

For the next two investigations, we will take this a step further.  Instead of looking at single inverse operations, we will examine inverse functions.  Here is an example of a pair of inverse functions:

We will determine what makes these inverse functions and how we can identify inverse functions.

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Let's look at some functions. We'll start easy.
If f(x) = x+4, evaluate f(5)=

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Now let's say we have the function g(x) = x-4, what is g(9)?

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If f(x)=5x, then what is f(3)?

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Now given function g(x) = x/5, what is g(15)?

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Given f(x) = 5x+2, evaluate f(3).

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If g(x) = (x-2)/5, then evaluate g(17).

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Look back at questions 2-7.
What do you notice about the relationship between f(x), and the g(x) function that followed?

Q#2-3 Q#4-5 Q#6-7
f(x) = x+4 f(x) = 5x f(x) = 5x+2
f(5) = 9 f(3) = 15 f(3) = 17

g(x) = x-4 g(x) = x/5 g(x) =(x-2)/5
g(9) = 5 g(15) = 3 g(17) = 3

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You may have noticed that the output of g(x) was the input of f(x), and the output of f(x) was the input of g(x).
When this relationship happens, it means that f(x) and g(x) are inverse functions.

For example : If f(x) was a machine that you put yarn into, and a sweater came out, then the inverse function would be a machine that you put a sweater into, and then yarn comes out.

Instead of using g(x) as the inverse function of f(x), we use the notation f -1(x). We say "f inverse of x". The inverse function of f(x) is f -1(x).

If f(7) = 11, then f -1(11)= ____

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With functions that contain only one operation, we can predict what the inverse function will be.

If f(x) = x-6, then what is f -1(x)?

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If f(x) = x/-4 , then what is f -1(x)?

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With more than one operation it can be a bit trickier.
If f(x) = 3x-7, then what is f -1(x)?

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If you could make your own non-math inverse machines what would they do?

Reminder: If you haven't taken the Unit 2 test, be sure to take it by Sunday. I'm available for questions today and Friday afternoon.

AA3-0 Inverse functions investigation

We already know that some operations "undo" other operations. We call these inverse operations. Match the operations below with their inverse operation:

Let's look at some functions. We'll start easy.If f(x) = x+4, evaluate f(5)=

Now let's say we have the function g(x) = x-4, what is g(9)?

If f(x)=5x, then what is f(3)?

Now given function g(x) = x/5, what is g(15)?

Given f(x) = 5x+2, evaluate f(3).

If g(x) = (x-2)/5, then evaluate g(17).

Look back at questions 2-7.What do you notice about the relationship between f(x), and the g(x) function that followed?Q#2-3 Q#4-5 Q#6-7 f(x) = x+4 f(x) = 5x f(x) = 5x+2f(5) = 9 f(3) = 15 f(3) = 17g(x) = x-4 g(x) = x/5 g(x) =(x-2)/5g(9) = 5 g(15) = 3 g(17) = 3

With functions that contain only one operation, we can predict what the inverse function will be. If f(x) = x-6, then what is f -1(x)?

If f(x) = x/-4 , then what is f -1(x)?

With more than one operation it can be a bit trickier. If f(x) = 3x-7, then what is f -1(x)?

If you could make your own non-math inverse machines what would they do?

We already know that some operations "undo" other operations. We call these inverse operations. Match the operations below with their inverse operation:

Let's look at some functions. We'll start easy.If f(x) = x+4, evaluate f(5)=

Now let's say we have the function g(x) = x-4, what is g(9)?

If f(x)=5x, then what is f(3)?

Now given function g(x) = x/5, what is g(15)?

Given f(x) = 5x+2, evaluate f(3).

If g(x) = (x-2)/5, then evaluate g(17).

Look back at questions 2-7.What do you notice about the relationship between f(x), and the g(x) function that followed?Q#2-3 Q#4-5 Q#6-7 f(x) = x+4 f(x) = 5x f(x) = 5x+2f(5) = 9 f(3) = 15 f(3) = 17g(x) = x-4 g(x) = x/5 g(x) =(x-2)/5g(9) = 5 g(15) = 3 g(17) = 3

With functions that contain only one operation, we can predict what the inverse function will be. If f(x) = x-6, then what is f -1(x)?

If f(x) = x/-4 , then what is f -1(x)?

With more than one operation it can be a bit trickier. If f(x) = 3x-7, then what is f -1(x)?

If you could make your own non-math inverse machines what would they do?

Let's look at some functions. We'll start easy.
If f(x) = x+4, evaluate f(5)=

Look back at questions 2-7.
What do you notice about the relationship between f(x), and the g(x) function that followed?

Q#2-3 Q#4-5 Q#6-7
f(x) = x+4 f(x) = 5x f(x) = 5x+2
f(5) = 9 f(3) = 15 f(3) = 17

g(x) = x-4 g(x) = x/5 g(x) =(x-2)/5
g(9) = 5 g(15) = 3 g(17) = 3

With functions that contain only one operation, we can predict what the inverse function will be.

If f(x) = x-6, then what is f -1(x)?

With more than one operation it can be a bit trickier.
If f(x) = 3x-7, then what is f -1(x)?

Let's look at some functions. We'll start easy.
If f(x) = x+4, evaluate f(5)=

Look back at questions 2-7.
What do you notice about the relationship between f(x), and the g(x) function that followed?

Q#2-3 Q#4-5 Q#6-7
f(x) = x+4 f(x) = 5x f(x) = 5x+2
f(5) = 9 f(3) = 15 f(3) = 17

g(x) = x-4 g(x) = x/5 g(x) =(x-2)/5
g(9) = 5 g(15) = 3 g(17) = 3

With functions that contain only one operation, we can predict what the inverse function will be.

If f(x) = x-6, then what is f -1(x)?

With more than one operation it can be a bit trickier.
If f(x) = 3x-7, then what is f -1(x)?