Question

Show that the function f : N → N defined by f(m) = m² + m + 3 is one-one function

Answer 1

N = {1, 2, 3, 4, 5, …..}

f(m) = m² + m + 3

f(1) = 1² + 1 + 3 = 5

f(2) = 2² + 2 + 3 = 9

f(3) = 3² + 3 + 3 = 15

f(4) = 4² + 4 + 3 = 23

f = {(1, 5) (2, 9) (3, 15) (4, 23)}

From the diagram we can understand different elements in (N) in the domain, there are different images in (N) co-domain.

∴ The function is a one-one function.