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What is a function?
A function is a combination of one or more mathematical operations that takes a set of numbers and changes them into another set of numbers.
What does the notation     indicate?
The notation    indicates a function , where is the input and is the output.
What is the input of a function?
The input of a function is the number being put into the function, often referred to as  .
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What is a function?
A function is a combination of one or more mathematical operations that takes a set of numbers and changes them into another set of numbers.
What does the notation     indicate?
The notation    indicates a function , where is the input and is the output.
What is the input of a function?
The input of a function is the number being put into the function, often referred to as  .
What is the output of a function?
The output of a function is the number coming out of the function, often referred to as or .
How would you find the value of for a function ?
To find the value of for a function , substitute into the equation of the function.
For example, if , then .
How would you find the value of if you knew that ?
To find the value of if you know that :
Set the equation for equal to 15
Then solve for
For example, if and , then
Define a composite function.
A composite function is a function that 'combines' two functions.
The output of one function is used as the input for the other function.
What does the notation mean?
is the notation for a composite function made up of functions and .
It means " is applied to the output of ".
I.e., first put into the function , and next put the output into the function .
Note that the function on the right () acts first, and the function on the left () acts second.
What does the notation mean?
is the notation for a composite function made up of functions and .
It means " is applied to the output of ".
I.e., first put into the function , and next put the output into the function .
Note that the function on the right () acts first, and the function on the left () acts second.
How would you find the value of ?
To find the value of :
First substitute into the equation for .
Then substitute the output into the equation for .
Give the definition of an inverse function.
An inverse function is a function that does the exact opposite operations of the function it came from.
What is the notation for the inverse function of the function ?
The notation for the inverse function of the function is .
What are the steps to find the inverse function of ?
To find :
Write as .
Swap and to get .
Rearrange to make the subject.
Replace with to rewrite as .
If you knew that , how would you find ?
An inverse function 'undoes' the operations of the original function.
So if turns 3 into 10, then turns 10 back into 3.
I.e., if , then .
What is equal to?
is a composite function of and its inverse .
An inverse function 'undoes' the operations of the original function (and vice versa).
So