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

So, f: A → B is One – One function

⇔ a≠b

⇒ f(a)≠f(b) for all a, b ∈ A

⇔ f(a) = f(b)

⇒ a = b for all a, b ∈ A

Onto Function: – A function f: A → B 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, f: A → B is Surjection iff for each b ∈ B, there exists a ∈ B such that f(a) = b

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

Now, f : R → R, defined by f(x) = sin²x + cos²x

Check for Injectivity and Check for Surjectivity

Let x be element belongs to R i.e x ∈ R such that

So, from definition

⇒ f(x) = sin²x + cos²x

⇒ f(x) = sin²x + cos²x

⇒ f(x) = 1

⇒ f(x) = constant

We know that a constant function is neither One – One function nor onto function.

Thus, It is not Bijective function