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FUNCTION, Not function-Function - Coggle Diagram
FUNCTION
TYPES OF FUNCTIONS
Onto Function
In mathematics, a function f from a set X to a set Y is surjective (also known as onto, or a surjection), if for every element y in the codomain Y of f, there is at least one element x in the domain X of f such that f(x) = y.
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One to one Function
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A function f is 1 -to- 1 if no two elements in the domain of f correspond to the same element in the range of f . In other words, each x in the domain has exactly one image in the range
Into Function
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Let f : A ----> B be a function. · There exists even a single element in B having no pre-image in A, then f is said to be an into function.
Identity Function in mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. That is, for f being identity, the equality f(x) = x holds for all x
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Even and Odd Function
Even Function
If powers of x are only even,then function is called even function.
Odd Function
If powers of x are only odd, then function is called odd function.
Piecewise Functions
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Piecewise function, the rule of the function differs for the disjoint subsets of the
domain.
Equal Function
In order to decide on the equality of two functions, the requirements are as follows; 1. The domain and the range of the functions must be equal. 2. The image of each element of the domain under both functions must be equal.
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2) if x is element of A and y is element of B then the relation can be expressed as f:x->y,f(x)=y
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Some function examples:
Example)f: R->R,f(x)=4x+3, A={0,1,2,3}.
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What is function?
If there is an output for each input, a unique output for each input than the relation satisfied by two variables called function
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