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, 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 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