Question:
Mark (√) against the correct answer in the following:
$f: N \rightarrow N: f(x)=x^{2}+x+1$ is
A. one - one and onto
B. one - one and into
C. many - one and onto
D. many - one and into
Solution:
In the given range of $N f(x)$ is monotonically increasing.
$\therefore f(x)=x^{2}+x+1$ is one one.
But Range of $f(n)=[0.75, \infty) \neq N$ (codomain)
Hence, $f(x)$ is not onto.
Hence, the function $f: N \rightarrow N: f(x)=\left(x^{2}+x+1\right)$ is one - one but not onto. i.e. into
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