Engineering
Mathematics
Composition of Functions
Question

Let N be the set of natural numbers and two functions f and g be defined as f, g: N → N such that f(n) ={n+12,if n is oddn2,if n is even  and g(n) = n – (– 1)n. Then fog is

neither one‑one nor onto

onto but not one‑one

one‑one but not onto

both one‑one and onto

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Solution

f(g(1))=1f(g(2))=1}  Many  one

f(g(2k))=k

f(g(2k+1))=k+1

∴ Onto