Page No 11:
Question 9:
Let f: N → N be defined by
State whether the function f is bijective. Justify your answer.
f: N → N is defined as
It can be observed that:
∴ f is not one-one.
Consider a natural number (n) in co-domain N.
Case I: n is odd
∴n = 2r + 1 for some r ∈ N. Then, there exists 4r + 1∈N such that
.
Case II: n is even
∴n = 2r for some r ∈ N. Then,there exists 4r ∈N such that
.
∴ f is onto.
Hence, f is not a bijective function.
