UPSEE Solved Model Paper 7

given :
f : N → N such that f (n) = (n+5)2 , n ∊ N
Now,
For one - one function
Let f(n1) = f(n2),n1,n2 ∊ N
⇒ (n1+5)2 = (n2+5)2
⇒ n12 + 25 + 10n1 = n22 + 25 + 10n2
⇒ (n1−n2)(n1+n2+10) = 0
⇒ n1 = n2
∴ f is one - one function
if we put n = 1 , 2 , 3 , 4 , ... ∞ , we get
f (1) = (1+5)2 = 36
f (2) = (5+2)2 = 49
f (3) = (3+5)2 = 64 ... etc
⇒ Range of f = (36 , 49 , 64 , ... ∞) ⊂ N
∴ f is not an onto function.
Hence, f is one-one but not onto.
Therefore, option 'D' is correct.