2.1 Recap on Functions

  1. What the the 3 things that make up a function?
    • The input
    • The transformation
    • The output
  2. 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.
  3. What do we call things that can go INTO a function or relation?
    f:A->B
    f(a)=b
    A is the Domain
  4. 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.
  5. 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.
  6. 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.
  7. 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
  8. What is the "relation" between a co-domain and a range?
    The range is a subset of the co-domain.
  9. 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.
  10. What is a relation?
    f:A->B
    it is some way of matching elements of a set A to another set B
  11. What is a function?
    EVERY element maps in A maps either to one or more elements in B.
  12. What is an Injective function?
    f:A->B
    • Injective means we won't have two or more "A"s pointing to the same "B".
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  13. What is an Surjective function?
    f:A->B
    • Image Upload 2
    • Surjective means that every "B" has at least one matching "A" (maybe more than one).
  14. What is an Surjective function?
    f:A->B
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    Bijective means both Injective and Surjective together.
  15. f:A->B
    f(a)=b

    What is the inverse function of f?
    it is f(b)=a where f´:B->A
  16. 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
  17. How do we solve the issues if any on each inverse?
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  18. Solve the composite function (g º f)(x)
    when f(x) = 2x+3 and g(x) = x2
    Image Upload 7
Author
ccc
ID
343040
Card Set
2.1 Recap on Functions
Description
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Updated