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