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Question

What are the properties of function?


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Solution

Properties of function:

Definition of function: A function is a relationship between two sets of data, one input and the other output. A relation is said to be a function if and only if each of the input data is related to exactly one output data.

Properties:

  1. Functions can either be decreasing, increasing, or constant.
  • A constant function is a function where the output remains the same regardless of the input values.
  • A function is said to be increasing if for every x1 and x2 that satisfies x2>x1, then fx2fx1. If the function is strictly greater than, then the function is strictly increasing.
  • A function is said to be decreasing if for every x1 and x2 that satisfies x2>x1, then fx2fx1. If the function is strictly less than, then the function is strictly decreasing.

2. A function f is injective if no two elements in the domain map to the same element in the co-domain.

If fa=fa',then a=a'

3. A function f is surjective if the range of f is equal to the codomain of f.

If bB,there exisis aA such that fa=b

4. A function f is bijective if it is both injective and surjective.


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