Onto (Surjective) FunctionĪ function f: X -> Y is said to be an onto function, if every element of Y is an image of some element of set X under f, i.e for every y ∈ Y there exists an element x in X such that f(x) = y. Check whether the function is Many to One or not?ĭomain = after mapping. Sample Examples on Many to One functionĮxample 1: f(x) = x 2. Property: One or more elements having the same image in the codomainĬondition to be Many to One function: One or more than one element in the domain having a single image in the codomain. If the function is not one to one function then it should be many to one function means every element of the domain has more than one image at codomain after mapping. Hence the function f(x) = 1/x is One to One. Since x 1 = x 2, means all elements of the domain are mapped with a single element of the codomain. We will check this too as we had done the above question. In question R -> R, where R belongs to Non-Zero Real Number, which means that the domain and codomain of the function are non zero real number. Then check whether the given function is One to One or not? Hence function f(x) = 2x + 1 is Injective (One to One).Įxample 5: If f: R -> R by f(x) = 1/x. For checking whether the function is injective or not, we can write the functions as, In question N -> N, where N belongs to Natural Number, which means that the domain and codomain of the function is a natural number. Hence the function f(x) = x 2 + 3 is not one to one function.Įxample 4: If N -> N, f(x) = 2x + 1 then check whether the function is injective or not? Now let’s check, we can write the function as, To check whether the function is One to One or not, we will follow the same procedure. Hence the function f(x) = 3x – 2 is one to one function.Įxample 3: Check whether the function is one to one or not: f(x) = x 2 + 3. Since both x 1 = x 2 means that elements of the domain having a single pre-image in its codomain. For checking, we can write the function as, To check the function is one to one or not, we have to check that elements of the domain are having only a single pre-image in codomain or not. Sample Examples on One to One (Injective) functionĮxample 1: Taking f(x) = 2x + 3, putting 1, 2, 1/2 in place of x.įrom the above image, we can conclude that our function f(x) is One to One because every element of the domain having a single image.Įxample 2: Check whether the function is one to one or not: f(x) = 3x – 2 Property: A function f: A -> B is one to one if for any f(x 1) = f(x 2) means x 1 = x 2, i.e, image of distinct element of A under f mapping (function) are distinct.Ĭondition to be One to One function: Every element of the domain has a single image with codomain after mapping. Thus, f is one to one iff f(x 1) = f(x 2).
Many to One Into Function One to One (Injective) functionĪ function f: X -> Y is said to be a one to one function if the images of distinct elements of X under f are distinct.One to One Onto Functions (Bijective Function).Second Order Derivatives in Continuity and Differentiability | Class 12 Maths.Difference between write() and writelines() function in Python.Torque on an Electric Dipole in Uniform Electric Field.Properties of Matrix Addition and Scalar Multiplication | Class 12 Maths.Graphs of Inverse Trigonometric Functions - Trigonometry | Class 12 Maths.
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