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FUNCTIONS - Coggle Diagram
FUNCTIONS
A function is a binary relation between two sets that associates every element of the first set to exactly one element of the second set. Typical examples are functions from integers to integers, or from the real numbers to real numbers.
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INTO FUNCTIONS
f: A --> B is the function. If f(A)≠B, f is an INTO function.
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ONE-TO-ONE FUNCTIONS
If the image of each element in the domain is different than one another, the function is called a ONE-TO-ONE function.
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If the function is f: A-->B, for f(a) = f(b), if a=b is satisfied, then f is a one-to-one function.
It is denoted as 1-1.
IDENTITY FUNCTIONS
Let's say A is a set. The function I: A-->A defined by l(x)=x for all x∈A is called IDENTITY FUNCTION.
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EQUAL FUNCTIONS
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In order to decide on the equality of two functions, these are the requirements:
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EVEN AND ODD FUNCTIONS
f: R-->R, for ∀x∈R
if f(-x) = f(x), then f is an even function.
if f(-x) = - f(x), then f is an odd function.
LINEAR FUNCTIONS
For any real numbers a and b,
f :R-->R, f(x) = y = ax+b is said to be linear function.
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𝐆𝐑𝐀𝐏𝐇𝐒 𝐎𝐅 𝐅𝐔𝐍𝐂𝐓𝐈𝐎𝐍𝐒
The set of the points in the analytic plane corresponding to the elements of a function is the graph of this function. Symbolically, given a function f: A-->B, the set f={(x, y): y = f(x), (x,y) ∈ AxB} is the graph of the function.
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COMPOSITION OF FUNCTIONS
Function composition is an operation that takes two functions f and g and produces a function h such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.
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If the functions f: A-->B and g: B-->C are 1-1, then the function gof: A-->C is also 1-1
If the functions f: A-->B and g: B-->C are onto, then the function
gof: A-->C is also onto.
INVERSE OF A FUNCTION
Inverse functions, in the most general sense, are functions that "reverse" each other.
f: A-->B, the function y=f(x) is given and it is 1-1 and onto. For x∈A, if whenever f(x)=y, f−1(y)=x, then the function f-1 is said to be inverse of the function f.
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