Let f : N → N be defined by f(x) = x² + x + 1. The function is:

Let f : N → N be defined by f(x) = x² + x + 1. The function is:

• A. one-one and onto
• B. one-one but not onto
• C. onto but not one-one
• D. neither one-one nor onto

Answer: B) one-one but not onto

Explanation: For x, y ∈ N, f(x) = f(y) → x² + x = y² + y → (x−y)(x+y+1) = 0 → x = y → one-one. f(1) = 3, f(2) = 7. 1, 2, 4, 5, 6... are not in range → not onto.