Question 6

**f:** odd n → 1,2,3,… ; even n → 1,0,−1,−2,… So f is onto ℤ but f(1)=f(2)=1, not one-one. (D) true. **g:** n≥0 → 3,5,7,… ; n<0 → 2,4,6,… So g is one-one but misses 1, not onto. (C) false. **g∘f:** not one-one (since f isn't), and its range misses 1 (g never gives 1), so not onto. (A) true. **f∘g:** g is injective onto ℕ∖{1}, and f restricted to ℕ∖{1} is a bijection onto ℤ, so f∘g is one-one and onto. (B) false.

No written reasoning was returned for this item.

No written reasoning was returned for this item.