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
⇒ 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
Now, Let, given by f(x) = 5
As we know
A constant function is neither one – one nor onto.
So, here f(x) = 5 is constant function
given by f(x) = 5 is neither one – one nor onto function.
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