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Home » Define each of the following: (i) injective function (ii) surjective function Give an example of each type of functions.
Define each of the following:
(i) injective function
(ii) surjective function
Give an example of each type of functions.
CBSE | Class 12 | Excercise 2A | Functions | Maths | RS Aggarwal
Define each of the following:
(i) injective function
(ii) surjective function
Give an example of each type of functions.

Solution:

(i) Injective function: It is, also known as one-one
function and is a type of function where every element in set A has an
image in set B.
Hence, f: A → B is one-one or injection function only if f(a) = f(b)
has a unique solution a = b.
For example: f(x) = 2x + 1 is injection for f: R \rightarrow R
f(x) = f(y)
⇒ 2x + 1 = 2y + 1
⇒ x = y

(ii) Surjective function: It is, also known as onto
function and is a function where for every element of set A, there is
atleast one image in set B, such that no element in Set B is left
without a match or ordered pair.
For example: f(x) = x^2 from the set of integers Z to the set of whole no. W is a surjective or onto function.

i

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