Solution: To prove that f is onto, we need to show that every element y in the range of f has at least one preimage x in the domain of f such that f(x) = y. Method I we take any element y in the range of function and then try to see if there exists an element in the domain of f such that f(x) = yĮxample: Let f: R-> R be defined by f(x) = 3x – 2. In other words, there are no elements in the range that are not mapped to by at least one element in the domain. To prove that a function is onto, also known as surjective, you need to show that every element in the range of the function has at least one preimage in the domain. Lets first start with the definition of the onto functions Definition of onto functionsĪ function f: A-> B is said to be onto(surjective) if every element of B is the image of some element of A under f, i,e for every $y \in B$, there exists a element x in A where f(x)=y how to prove onto function This post we will see given a function, how to check if it is onto function or not.
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