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2.1 Recap on Functions
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What the the 3 things that make up a function?
The input
The transformation
The output
What are the two rules that must be followed for a function to be called a function?
Otherwise it is just a relation.
Give example of f:A->B
1. EVERY element in A must be mapped to some element in Y by the function.
3. One-to-One or Many-to-One allowed but not Many-to-One.
What do we call things that can go INTO a function or relation?
f:A->B
f(a)=b
A is the Domain
What do we call things that MAY possibly come out as a result from using the function/relation?
f:A->B
f(a)=b
B is called the CO-domain.
What do we call things that actually come out as a result from using the function/relation?
f:A->B
f(a)=b
All b´s are called the the range.
When are two function/relations equal?
Two functions are equal if their domain and co-domain are equal, and if the image of both functions is the same for each element in the domain.
What is the image and the pre-image in the following relation?
f:A->B
f(a)=b
a is the pre-image of b
b is the image of a
fokuserar man på a är är a pre image för att inte transformetat elementet ännu
fokurerar man på b så är b bilden av a då man transformerat a för att få b
What is the "relation" between a co-domain and a range?
The range is a subset of the co-domain.
Why is the sqrroot not a function?
If we say that the function/relation has the domain of all real numbers?
Because f then could map as a one-to-many function; f(9) = -3 or 3.
What is a relation?
f:A->B
it is some way of matching elements of a set A to another set B
What is a function?
EVERY element maps in A maps either to one or more elements in B.
What is an Injective function?
f:A->B
Injective means we won't have two or more "A"s pointing to the same "B".
What is an Surjective function?
f:A->B
Surjective means that every "B" has at least one matching "A" (maybe more than one).
What is an Surjective function?
f:A->B
Bijective means both Injective and Surjective together.
f:A->B
f(a)=b
What is the inverse function of f?
it is f(b)=a where f´:B->A
How can we solve for the inverse of function?
"f(x)=2x+3" ?
Replace the old function with a new variable y and solve for x variable;
f(x)=2x+3
y=2x+3
y-3=2x
(y-3)/2=x
f´(y)=(y-3)/2
How do we solve the issues if any on each inverse?
Solve the composite function (g º f)(x)
when f(x) = 2x+3 and g(x) = x2
Author
ccc
ID
343040
Card Set
2.1 Recap on Functions
Description
NuDå
Updated
2018-10-17T20:12:21Z
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