TIP: – One – One Function: – A function is said to be a one – one functions or an injection if different elements of A have different images in B.

So, is One – One function

⇔ a≠b

⇒ f(a)≠f(b) for all

⇔ f(a) = f(b)

⇒ a = b for all

Onto Function: – A function is said to be a onto function or surjection if every element of A i.e, if f(A) = B or range of f is the co – domain of f.

So, is Surjection iff for each , there exists such that f(a) = b

Bijection Function: – A function is said to be a bijection function if it is one – one as well as onto function.

Now, here f: A → A: A = [–1, 1] given by function is

Check for Injectivity:

Let x, y be elements belongs to A i.e. such that

⇒ f(x) = f(y)

⇒

⇒ 2x = 2y

⇒ x = y

1 belongs to A then

Not element of A co – domain

Hence, f is not One – One function

Check for Surjectivity:

Let y be element belongs to A i.e be arbitrary, then

⇒ f(x) = y

⇒

⇒ x = 2y

Now,

1 belongs to A

⇒ x = 2, which not belong to A co – domain

Hence, f is not onto function

Thus, It is not Bijective function