Prove that the function \(f: \mathbb{N} \rightarrow \mathbb{N}\) defined by \(f(m) = m^2 + m + 9\) is one-to-one function.
Proof:
\(N = \{1, 2, 3, 4, 5, ...\}\)
\(f(m) = m^2 + m + 9\)
\(f(1) =\)
\(f(2) =\)
\(f(3) =\)
\(f(4) =\)
Thus, we can understand that there are different images in the co-domain for different elements in the domain.
Thus, the function \(f\) is .
Hence, we proved.
Answer variants:
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a one-to-one function
not a one-to-one function
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