# 2.1 Recap on Functions

 .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } What the the 3 things that make up a function? The input The transformationThe 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 bb is the image of a fokuserar man på a är är a pre image för att inte transformetat elementet ännufokurerar 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+3y=2x+3y-3=2x(y-3)/2=xf´(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 .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } Authorccc ID343040 Card Set2.1 Recap on Functions DescriptionNuDå Updated2018-10-17T20:12:21Z Show Answers