Functions Flashcards
What is an inverse function of a certain function?
A function is another’s inverse if it undoes the latter
ex. F(3)=2 and F(2)^-1=3
What causes a function to have no inverse function?
If the first function has multiple x-values for one y-value
ex. F(2)= 5 and F(10)= 5 so F(x) has no inverse
List the order of operations for the inverse function of F(x)=2(x+3)-5?
- add five
- divide by 2
- subtract 3
What would happen to the inverse of a function that first squares the x-value?
The inverse would have two possible answers for one x input
What is a relation?
a mapping from one set to the other; does not have to be a function
What is a set of inputs called?
A domain
What is a set of outputs called?
A range
What is a set?
A collection of elements
What type of relation is a function?
A function is a relation where each input has exactly one input.
What is a binary operation?
An operation that works on two elements if a set
ex. F(3)+G(2)= 11
True or False: The composition of functions is commutative
False
What are the natural numbers?
Natural numbers are the positive integers
True or False: Natural numbers are closed under subtraction but not under addition.
False; They are closed under addition but not under subtraction
What does it mean for a set to be CLOSED under a certain operation?
Every element of the set will remain part of the set when going through the given operation if that set is closed under that same operation
What are the rational numbers?
The rational numbers are the positive and negative quotients of two integers.
