# Mark (√) against the correct answer in the following:

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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