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FUNCTIONS - Coggle Diagram
FUNCTIONS
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Function Or Not?
1)Every element in the domain is related with an element in the range.
2) Any element in the domain must be related to only one element in the range.
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Types Of Functions
Into Functions
Let A→B be a function. If f(A) ≠ B, f is said to be 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.
This can be expressed mathematically as;
For a function f:A→B for any a, b ∈ A,
for a ≠ b if (a) ≠ f(b) is satified, then f is a one to one function.
This can also be expressed as,
for f(a) = f(b), if a=b is satisfied, then f is a one to one function.
It is denoted as 1-1.
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*Constant Function *
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Given f: A→B, if f maps all the elements of set A to one and only one element of set B, this function is called as a constant function and is denoted by f(x)=c where c is a constant real number.
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Linear Function
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For any real numbers a and b, f:R→R, f(x) = y = ax+b is said to be linear function.
If f is a linear function, then its graph is a line.
Piecewise Function
It is is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain.
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NOTE that in the piecewise function, the rule of the function differs for the disjoint subsets of the domain.
Graphs Of The Function
The set of the point analyric 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 this function.
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Linear Function
M and b is a real number, if m≠0, f(x) = mx+b a function defined by its equation is called a linear function.
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Constant Function
A function that corresponds to every real number x to the same real number b is called a constant function.
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Composition of Function
Function composition is an operation that takes two functions f and g and produces a function h such that h(x) = g(f(x)).
The resulting composite function is denoted g ∘ f : X → Z, defined by (g ∘ f )(x) = g(f(x)) for all x in X.
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Inverse of a Function
f: A→B , the function y = f(x) is given and it is 1-1 and onto. For x e A, if whenever f(x) = y, f(Mines ¹)(y) = x, then the function f(Mines¹) is said to be inverse of the function f. f(Mines¹) is a function defined from the set B to the set
A.
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