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please tell me various methods to check onto function

please tell me various methods to check onto function


1 Answers

Ramesh V
70 Points
11 years ago

A function f from A to B is called onto if for all b in B there is an a in A such that f (a) = b.All elements in B are used.

Such functions are referred to as surjective.

An example is shown below:

When working in the coordinate plane, the sets A  and B  become the Real numbers, stated as f: R--->R.

This means that for every element in the codomain there exists an element in the domain which maps to it. The method used to establish this property depends on how the function is given and its properties.

Let y be any element of the codomain and x an element of the domain. We solve the equation y = f(x) for x. This gives us a possible candidate for a domain element. We prove it is a suitable domain element by substituting this value into the function.                                                                 As an example, let's prove that f:R-->R defined by f(x) = 3x-4 is onto, where R denotes the real numbers. We let y be a typical element of the codomain and set up the equation y =f(x). then, y = 3x-4 and solving for x we get x =(y+4)/3. Since y is a real number,                                                then (y+4)/3 is a real number and f((y+4)/3) = 3(y+4)/3 -4 = y.


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Naga Ramesh
IIT Kgp - 2005 batch



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